Example Usage

This example is a reproduction of Figure 1 from http://doi.org/10.1098/rspa.2007.1900 :

The original figure:

Code to reproduce the above figure as close as possible:

# Typical imports: Matplotlib, numpy, sklearn and of course our mf2 package
import matplotlib.pyplot as plt
import mf2
import numpy as np
from sklearn.gaussian_process import GaussianProcessRegressor as GPR
from sklearn.gaussian_process import kernels

# Setting up
low_x = np.linspace(0, 1, 11).reshape(-1, 1)
high_x = low_x[[0, 4, 6, 10]]
diff_x = high_x

low_y = mf2.forrester.low(low_x)
high_y = mf2.forrester.high(high_x)
scale = 1.87  # As reported in the paper
diff_y = np.array([(mf2.forrester.high(x) - scale * mf2.forrester.low(x))[0]
                   for x in diff_x])

# Training GP models
kernel = kernels.ConstantKernel(constant_value=1.0) \
         * kernels.RBF(length_scale=1.0, length_scale_bounds=(1e-1, 10.0))

gp_direct = GPR(kernel=kernel).fit(high_x, high_y)
gp_low = GPR(kernel=kernel).fit(low_x, low_y)
gp_diff = GPR(kernel=kernel).fit(diff_x, diff_y)

# Using a simple function to combine the two models
def co_y(x):
    return scale * gp_low.predict(x) + gp_diff.predict(x)

# And finally recreating the plot
plot_x = np.linspace(start=0, stop=1, num=501).reshape(-1, 1)
plt.figure(figsize=(6, 5), dpi=600)
plt.plot(plot_x, mf2.forrester.high(plot_x), linewidth=2, color='black', label='$f_e$')
plt.plot(plot_x, mf2.forrester.low(plot_x), linewidth=2, color='black', linestyle='--',
         label='$f_c$')
plt.scatter(high_x, high_y, marker='o', facecolors='none', color='black', label='$y_e$')
plt.scatter(low_x, low_y, marker='s', facecolors='none', color='black', label='$y_c$')
plt.plot(plot_x, gp_direct.predict(plot_x), linewidth=1, color='black', linestyle='--',
         label='kriging through $y_e$')
plt.plot(plot_x, co_y(plot_x), linewidth=1, color='black', label='co-kriging')
plt.xlim([0, 1])
plt.ylim([-10, 20])
plt.xlabel('$x$')
plt.ylabel('$y$')
plt.legend(loc=2)
plt.tight_layout()
plt.savefig('../_static/recreating-forrester-2007.png')
plt.show()

Reproduced figure: