def test_predict_output(self):
d, n = (3, 10)
sx = LHS(
xlimits=np.repeat(np.atleast_2d([0.0, 1.0]), d, axis=0),
criterion="m",
random_state=42,
)
x = sx(n)
sy = LHS(
xlimits=np.repeat(np.atleast_2d([0.0, 1.0]), 1, axis=0),
criterion="m",
random_state=42,
)
y = sy(n)
y = y.flatten()
kriging = MGP(n_comp=2)
kriging.set_training_values(x, y)
kriging.train()
x_fail_1 = np.asarray([0, 0, 0, 0])
x_fail_2 = np.asarray([0])
self.assertRaises(ValueError, lambda: kriging.predict_values(x_fail_1))
self.assertRaises(ValueError, lambda: kriging.predict_values(x_fail_2))
self.assertRaises(ValueError, lambda: kriging.predict_variances(x_fail_1))
self.assertRaises(ValueError, lambda: kriging.predict_variances(x_fail_2))
x_1 = np.atleast_2d([0, 0, 0])
var = kriging.predict_variances(x_1)
var_1 = kriging.predict_variances(x_1, True)
self.assertEqual(var, var_1[0])
def test_predict_output(self):
x = np.random.random((10, 3))
y = np.random.random((10))
kriging = MGP(n_comp=2)
kriging.set_training_values(x, y)
kriging.train()
x_fail_1 = np.asarray([0, 0, 0, 0])
x_fail_2 = np.asarray([0])
self.assertRaises(ValueError, lambda: kriging.predict_values(x_fail_1))
self.assertRaises(ValueError, lambda: kriging.predict_values(x_fail_2))
self.assertRaises(ValueError,
lambda: kriging.predict_variances(x_fail_1))
self.assertRaises(ValueError,
lambda: kriging.predict_variances(x_fail_2))
x_1 = np.atleast_2d([0, 0, 0])
var = kriging.predict_variances(x_1)
var_1 = kriging.predict_variances(x_1, True)
self.assertEqual(var, var_1[0])
def test_mgp(self):
import numpy as np
import matplotlib.pyplot as plt
from smt.surrogate_models import MGP
from smt.sampling_methods import LHS
# Construction of the DOE
dim = 3
def fun(x):
import numpy as np
res = (np.sum(x, axis=1)**2 - np.sum(x, axis=1) + 0.2 *
(np.sum(x, axis=1) * 1.2)**3)
return res
sampling = LHS(xlimits=np.asarray([(-1, 1)] * dim), criterion="m")
xt = sampling(8)
yt = np.atleast_2d(fun(xt)).T
# Build the MGP model
sm = MGP(
theta0=[1e-2],
print_prediction=False,
n_comp=1,
)
sm.set_training_values(xt, yt[:, 0])
sm.train()
# Get the transfert matrix A
emb = sm.embedding["C"]
# Compute the smallest box containing all points of A
upper = np.sum(np.abs(emb), axis=0)
lower = -upper
# Test the model
u_plot = np.atleast_2d(np.arange(lower, upper, 0.01)).T
x_plot = sm.get_x_from_u(u_plot) # Get corresponding points in Omega
y_plot_true = fun(x_plot)
y_plot_pred = sm.predict_values(u_plot)
sigma_MGP, sigma_KRG = sm.predict_variances(u_plot, True)
u_train = sm.get_u_from_x(xt) # Get corresponding points in A
# Plots
fig, ax = plt.subplots()
ax.plot(u_plot, y_plot_pred, label="Predicted")
ax.plot(u_plot, y_plot_true, "k--", label="True")
ax.plot(u_train, yt, "k+", mew=3, ms=10, label="Train")
ax.fill_between(
u_plot[:, 0],
y_plot_pred - 3 * sigma_MGP,
y_plot_pred + 3 * sigma_MGP,
color="r",
alpha=0.5,
label="Variance with hyperparameters uncertainty",
)
ax.fill_between(
u_plot[:, 0],
y_plot_pred - 3 * sigma_KRG,
y_plot_pred + 3 * sigma_KRG,
color="b",
alpha=0.5,
label="Variance without hyperparameters uncertainty",
)
ax.set(xlabel="x", ylabel="y", title="MGP")
fig.legend(loc="upper center", ncol=2)
fig.tight_layout()
fig.subplots_adjust(top=0.74)
plt.show()
