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 6.786680863e-09 2.218151080e-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 1.551467973e-11 2.217740430e-13
Iteration (num., iy, grad. norm, func.) : 0 0 1.401077818e-11 2.190113743e-13
Iteration (num., iy, grad. norm, func.) : 1 0 4.566246092e-10 1.398094006e-13
Iteration (num., iy, grad. norm, func.) : 2 0 3.187142258e-10 9.327244974e-14
Iteration (num., iy, grad. norm, func.) : 3 0 9.374199098e-11 2.441319143e-14
Iteration (num., iy, grad. norm, func.) : 4 0 7.181676598e-11 1.894335409e-14
Iteration (num., iy, grad. norm, func.) : 5 0 2.109617230e-11 1.047182645e-14
Iteration (num., iy, grad. norm, func.) : 6 0 8.050659814e-12 9.103083561e-15
Iteration (num., iy, grad. norm, func.) : 7 0 2.350748228e-12 8.576088440e-15
Iteration (num., iy, grad. norm, func.) : 8 0 6.944357725e-13 8.476438536e-15
Iteration (num., iy, grad. norm, func.) : 9 0 2.304594377e-13 8.459868871e-15
Iteration (num., iy, grad. norm, func.) : 10 0 2.613552317e-13 8.459867906e-15
Iteration (num., iy, grad. norm, func.) : 11 0 7.561345920e-14 8.454412587e-15
Iteration (num., iy, grad. norm, func.) : 12 0 2.392678153e-14 8.453533882e-15
Iteration (num., iy, grad. norm, func.) : 13 0 6.369300553e-15 8.453334168e-15
Iteration (num., iy, grad. norm, func.) : 14 0 1.376985434e-15 8.453277655e-15
Iteration (num., iy, grad. norm, func.) : 15 0 9.337089436e-16 8.453273240e-15
Iteration (num., iy, grad. norm, func.) : 16 0 7.890066819e-16 8.453272942e-15
Iteration (num., iy, grad. norm, func.) : 17 0 6.756594233e-16 8.453271528e-15
Iteration (num., iy, grad. norm, func.) : 18 0 2.143825648e-16 8.453270718e-15
Iteration (num., iy, grad. norm, func.) : 19 0 7.115441072e-17 8.453270419e-15
Solving for output 0 - done. Time (sec): 0.1149590
Solving nonlinear problem (n=100) - done. Time (sec): 0.1149590
Solving for degrees of freedom - done. Time (sec): 0.1149590
Training - done. Time (sec): 0.1149590
___________________________________________________________________________
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 1.672771647e-10 2.493685484e-14
Solving for output 0 - done. Time (sec): 0.0166364
Solving initial startup problem (n=82) - done. Time (sec): 0.0166364
Solving nonlinear problem (n=82) ...
Solving for output 0 ...
Iteration (num., iy, grad. norm, func.) : 0 0 7.484144240e-12 2.493684372e-14
Iteration (num., iy, grad. norm, func.) : 0 0 9.032459200e-12 2.483317928e-14
Iteration (num., iy, grad. norm, func.) : 1 0 8.718228593e-11 2.392796282e-14
Iteration (num., iy, grad. norm, func.) : 2 0 4.084733341e-11 1.653726244e-14
Iteration (num., iy, grad. norm, func.) : 3 0 3.968335331e-11 1.635461268e-14
Iteration (num., iy, grad. norm, func.) : 4 0 1.075192906e-11 1.163951275e-14
Iteration (num., iy, grad. norm, func.) : 5 0 2.996703771e-12 1.114623030e-14
Iteration (num., iy, grad. norm, func.) : 6 0 4.613969124e-13 1.109347169e-14
Iteration (num., iy, grad. norm, func.) : 7 0 9.192134677e-14 1.109036961e-14
Iteration (num., iy, grad. norm, func.) : 8 0 5.561355733e-14 1.108986678e-14
Iteration (num., iy, grad. norm, func.) : 9 0 1.518497445e-14 1.108946807e-14
Iteration (num., iy, grad. norm, func.) : 10 0 3.525949088e-15 1.108940914e-14
Iteration (num., iy, grad. norm, func.) : 11 0 4.977597964e-16 1.108940364e-14
Iteration (num., iy, grad. norm, func.) : 12 0 4.328767946e-17 1.108940341e-14
Solving for output 0 - done. Time (sec): 0.0814357
Solving nonlinear problem (n=82) - done. Time (sec): 0.0814357
Solving for degrees of freedom - done. Time (sec): 0.0980721
Training - done. Time (sec): 0.0980721
___________________________________________________________________________
Evaluation
# eval points. : 500
Predicting ...
Predicting - done. Time (sec): 0.0000000
Prediction time/pt. (sec) : 0.0000000
