def kPLSK(xt, yt, xtest, ytest):
########### The KPLSK model
# 'n_comp' and 'theta0' must be an integer in [1,ndim[ and a list of length n_comp, respectively.
t = KPLSK(n_comp=2, theta0=[1e-2, 1e-2], print_prediction=False)
t.set_training_values(xt, yt)
t.train()
print('KPLSK, err: ' + str(compute_rms_error(t, xtest, ytest)))
title = 'KPLSK model: validation of the prediction model'
return t, title, xtest, ytest
def test_kplsk(self):
import numpy as np
import matplotlib.pyplot as plt
from smt.surrogate_models import KPLSK
xt = np.array([0.0, 1.0, 2.0, 3.0, 4.0])
yt = np.array([0.0, 1.0, 1.5, 0.9, 1.0])
sm = KPLSK(theta0=[1e-2])
sm.set_training_values(xt, yt)
sm.train()
num = 100
x = np.linspace(0.0, 4.0, num)
y = sm.predict_values(x)
# estimated variance
s2 = sm.predict_variances(x)
# derivative according to the first variable
dydx = sm.predict_derivatives(xt, 0)
plt.plot(xt, yt, "o")
plt.plot(x, y)
plt.xlabel("x")
plt.ylabel("y")
plt.legend(["Training data", "Prediction"])
plt.show()
# add a plot with variance
plt.plot(xt, yt, "o")
plt.plot(x, y)
plt.fill_between(
np.ravel(x),
np.ravel(y - 3 * np.sqrt(s2)),
np.ravel(y + 3 * np.sqrt(s2)),
color="lightgrey",
)
plt.xlabel("x")
plt.ylabel("y")
plt.legend(["Training data", "Prediction", "Confidence Interval 99%"])
plt.show()
def test_kplsk(self):
import numpy as np
import matplotlib.pyplot as plt
from smt.surrogate_models import KPLSK
xt = np.array([0.0, 1.0, 2.0, 3.0, 4.0])
yt = np.array([0.0, 1.0, 1.5, 0.5, 1.0])
sm = KPLSK(theta0=[1e-2])
sm.set_training_values(xt, yt)
sm.train()
num = 100
x = np.linspace(0.0, 4.0, num)
y = sm.predict_values(x)
yy = sm.predict_derivatives(xt, 0)
plt.plot(xt, yt, "o")
plt.plot(x, y)
plt.xlabel("x")
plt.ylabel("y")
plt.legend(["Training data", "Prediction"])
plt.show()
def test_kplsk(self):
import numpy as np
import matplotlib.pyplot as plt
from smt.surrogate_models import KPLSK
xt = np.array([0., 1., 2., 3., 4.])
yt = np.array([0., 1., 1.5, 0.5, 1.0])
sm = KPLSK(theta0=[1e-2])
sm.set_training_values(xt, yt)
sm.train()
num = 100
x = np.linspace(0., 4., num)
y = sm.predict_values(x)
yy = sm.predict_derivatives(xt, 0)
plt.plot(xt, yt, 'o')
plt.plot(x, y)
plt.xlabel('x')
plt.ylabel('y')
plt.legend(['Training data', 'Prediction'])
plt.show()