def gEKPLS(xt, yt, xtest, ytest, funXLimits, ndim):
# 'n_comp' must be an integer in [1,ndim[, 'theta0' a list of n_comp values
t = GEKPLS(n_comp=2,
theta0=[1e-2, 1e-2],
xlimits=funXLimits,
delta_x=1e-2,
extra_points=1,
print_prediction=False)
t.set_training_values(xt, yt)
# Add the gradient information
for i in range(ndim):
t.set_training_derivatives(xt, yt[:, 1 + i].reshape((yt.shape[0], 1)),
i)
t.train()
# Prediction of the validation points
y = t.predict_values(xtest)
print('GEKPLS1, err: ' + str(compute_rms_error(t, xtest, ytest)))
title = ('GEKPLS model')
return t, title, xtest, ytest
# Prediction of the derivatives with regards to each direction space
yd_prediction = np.zeros((ntest, ndim))
for i in range(ndim):
yd_prediction[:, i] = t.predict_derivatives(xtest, kx=i).T
print('GEKPLS1, err of the ' + str(i + 1) + '-th derivative: ' +
str(compute_rms_error(t, xtest, ydtest[:, i], kx=i)))
if plot_status:
plt.plot(ydtest[:, i], ydtest[:, i], '-.')
plt.plot(ydtest[:, i], yd_prediction[:, i], '.')
if plot_status:
plt.show()
def test_gekpls(self):
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from smt.surrogate_models import GEKPLS
from smt.problems import Sphere
from smt.sampling_methods import LHS
# Construction of the DOE
fun = Sphere(ndim=2)
sampling = LHS(xlimits=fun.xlimits, criterion="m")
xt = sampling(20)
yt = fun(xt)
# Compute the gradient
for i in range(2):
yd = fun(xt, kx=i)
yt = np.concatenate((yt, yd), axis=1)
# Build the GEKPLS model
n_comp = 2
sm = GEKPLS(
theta0=[1e-2] * n_comp,
xlimits=fun.xlimits,
extra_points=1,
print_prediction=False,
n_comp=n_comp,
)
sm.set_training_values(xt, yt[:, 0])
for i in range(2):
sm.set_training_derivatives(xt, yt[:, 1 + i].reshape((yt.shape[0], 1)), i)
sm.train()
# Test the model
X = np.arange(fun.xlimits[0, 0], fun.xlimits[0, 1], 0.25)
Y = np.arange(fun.xlimits[1, 0], fun.xlimits[1, 1], 0.25)
X, Y = np.meshgrid(X, Y)
Z = np.zeros((X.shape[0], X.shape[1]))
for i in range(X.shape[0]):
for j in range(X.shape[1]):
Z[i, j] = sm.predict_values(
np.hstack((X[i, j], Y[i, j])).reshape((1, 2))
)
fig = plt.figure()
ax = fig.gca(projection="3d")
surf = ax.plot_surface(X, Y, Z)
plt.show()
def dEKPLS(xt, yt, xtest, ytest, funXLimits, ndim):
# 'n_comp' must be an integer in [1,ndim[, 'theta0' a list of n_comp values
t = GEKPLS(n_comp=1,
theta0=[1e-2],
xlimits=funXLimits,
delta_x=1e-2,
extra_points=1,
print_prediction=False)
t.set_training_values(xt, yt)
# Add the gradient information
for i in range(ndim):
t.set_training_derivatives(xt, yt[:, 1 + i].reshape((yt.shape[0], 1)),
i)
t.train()
title = 'GEKPLS model'
return t, title, xtest, ytest