def cokriging(i):
# Xt_e = np.array([[1.57894737, 17.8947368],
# [8.42105263, 17.8947368],
# [1.57894737, 2.10526316],
# [8.42105263, 2.10526316],
# ])
Xt_e = np.array([
[50.0891841, 11.000994],
[49.9108168, 38.999006],
[84.200043, 41.5655806],
[16.0943345, 7.97111717],
[15.7955774, 41.584603],
[83.9713379, 7.94023456],
])
Xt_c = arr_xy_low
yt_e = arr_stress_high_train[i]
yt_c = np.array(low_predict_data_by_force()[0][i])
sm = MFK(theta0=np.array(Xt_e.shape[1] * [1.0]), print_global=False)
sm.set_training_values(Xt_c, yt_c, name=0)
sm.set_training_values(Xt_e, yt_e)
sm.train()
Xp = arr_xy_high
y = sm.predict_values(Xp)
# MSE = sm.predict_variances(Xp)
# der = sm.predict_derivatives(Xp, kx=0)
return y.flatten()
def run_mfk_example(self):
import numpy as np
import matplotlib.pyplot as plt
from smt.applications import MFK
# Define the
def LF_function(x):
import numpy as np
return (0.5 * ((x * 6 - 2)**2) * np.sin(
(x * 6 - 2) * 2) + (x - 0.5) * 10.0 - 5)
def HF_function(x):
import numpy as np
return ((x * 6 - 2)**2) * np.sin((x * 6 - 2) * 2)
# Problem set up
ndim = 1
Xt_e = np.linspace(0, 1, 4, endpoint=True).reshape(-1, ndim)
Xt_c = np.linspace(0, 1, 11, endpoint=True).reshape(-1, ndim)
nt_exp = Xt_e.shape[0]
nt_cheap = Xt_c.shape[0]
# Evaluate the HF and LF functions
yt_e = HF_function(Xt_e)
yt_c = LF_function(Xt_c)
sm = MFK(theta0=np.array(Xt_e.shape[1] * [1.0]))
# low-fidelity dataset names being integers from 0 to level-1
sm.set_training_values(Xt_c, yt_c, name=0)
# high-fidelity dataset without name
sm.set_training_values(Xt_e, yt_e)
# train the model
sm.train()
x = np.linspace(0, 1, 101, endpoint=True).reshape(-1, 1)
# query the outputs
y = sm.predict_values(x)
MSE = sm.predict_variances(x)
der = sm.predict_derivatives(x, kx=0)
plt.figure()
plt.plot(x, HF_function(x), label="reference")
plt.plot(x, y, linestyle="-.", label="mean_gp")
plt.scatter(Xt_e, yt_e, marker="o", color="k", label="HF doe")
plt.scatter(Xt_c, yt_c, marker="*", color="g", label="LF doe")
plt.legend(loc=0)
plt.ylim(-10, 17)
plt.xlim(-0.1, 1.1)
plt.xlabel(r"$x$")
plt.ylabel(r"$y$")
plt.show()
print(Xt_e.shape[1] * [1.0]) # low-fidelity dataset names being integers from 0 to level-1 sm.set_training_values(Xt_c, yt_c, name=0) print(Xt_c) # high-fidelity dataset without name sm.set_training_values(Xt_e, yt_e) print(Xt_e) # train the model sm.train() x = np.linspace(0, 1, 101, endpoint=True).reshape(-1, 1) # query the outputs y = sm.predict_values(x) MSE = sm.predict_variances(x) der = sm.predict_derivatives(x, kx=0) plt.figure() plt.plot(x, HF_function(x), label="reference") plt.plot(x, LF_function(x), label="reference") plt.plot(x, y, linestyle="-.", label="mean_gp") plt.scatter(Xt_e, yt_e, marker="o", color="k", label="HF doe") plt.scatter(Xt_c, yt_c, marker="*", color="g", label="LF doe") plt.legend(loc=0) plt.ylim(-10, 17) plt.xlim(-0.1, 1.1) plt.xlabel(r"$x$")