def demo_2D():
# Create a Gaussian Process
x_training = np.array([
[0., 0.],
[1.5, 1.5],
[3., 3.],
[0., 1.5],
[1.5, 0.],
[0., 3.],
[3., 0.],
[3., 1.5],
[1.5, 3.]
])
y_training = get_y_simulated_2D(x_training)
gp = GaussianProcess(x_training, y_training)
np.random.seed(47)
gp = fit_GP_MAP(gp)
# Define observation
obs = [0.1, 0.0004]
# Coords to predict
n_rand = 2000
a_predict_min = 0
a_predict_max = np.pi
b_predict_min = a_predict_min
b_predict_max = a_predict_max
a_predict = np.random.rand(n_rand) * (a_predict_max - a_predict_min) + a_predict_min
b_predict = np.random.rand(n_rand) * (b_predict_max - b_predict_min) + b_predict_min
x_predict = np.concatenate((a_predict[:,None], b_predict[:,None]), axis=1)
x_predict = np.concatenate((x_predict, x_training), axis=0)
coords = x_predict
# Compute GPE expectations
expectations = gp.predict(coords)
# Compute Implausbility
hm = HistoryMatching(obs=obs, expectations=expectations)
I = hm.get_implausibility()
NROY = hm.get_NROY()
RO = hm.get_RO()
print("Fraction of points ruled out {:6}".format(str(float(len(RO))/float(n_rand))))
# Plotting
if makeplots:
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
Axes3D.scatter( # Training Data
ax,
x_training[:,0],
x_training[:,1],
y_training,
color='black',
marker = '.',
s = 100
)
#Axes3D.scatter( # GPE prediction
# ax,
# coords[:,0],
# coords[:,1],
# expectations[0],
# color='red',
# marker='.',
# s=2
#)
Axes3D.scatter( # GPE prediction uncertainty
ax,
coords[:,0][RO],
coords[:,1][RO],
expectations[0][RO] + 3*np.sqrt(expectations[1][RO]),
color='red',
marker='.',
s=1
)
Axes3D.scatter(
ax,
coords[:,0][RO],
coords[:,1][RO],
expectations[0][RO] - 3*np.sqrt(expectations[1][RO]),
color='red',
marker='.',
s=1
)
Axes3D.scatter(
ax,
coords[:,0][NROY],
coords[:,1][NROY],
expectations[0][NROY] + 3*np.sqrt(expectations[1][NROY]),
color='green',
marker='.',
s=1
)
Axes3D.scatter(
ax,
coords[:,0][NROY],
coords[:,1][NROY],
expectations[0][NROY] - 3*np.sqrt(expectations[1][NROY]),
color='green',
marker='.',
s=1
)
Axes3D.set(
ax,
xlabel = 'Input parameter a',
ylabel = 'Input parameter b',
zlabel = 'Model output f(a, b)'
)
plt.savefig('histmatch_2D.png', bbox_inches = "tight")
