y_m = np.mean(y, axis=0)
y_s = np.std(y, axis=0)
y = Normalize(y, y_m, y_s)
y_star = Normalize(y_star, y_m, y_s)
ModelInfo.update({"X": X})
ModelInfo.update({"y": y})
# Training
train()
# Prediction
mean_star, var_star = predict(X_star)
# Plot Results
Z = ModelInfo["Z"]
m = ModelInfo["m"]
plt.figure(1)
plt.plot(X, y, 'b+', alpha=0.1)
plt.plot(Z, m, 'ro', alpha=1)
plt.plot(X_star, y_star, 'b-')
plt.plot(X_star, mean_star, 'r--')
lower = mean_star - 2.0 * np.sqrt(var_star)
upper = mean_star + 2.0 * np.sqrt(var_star)
plt.fill_between(X_star.flatten(),
lower.flatten(),
upper.flatten(),
facecolor='orange',
alpha=0.5)
mean_star, var_star = pgp.predict(X_star)
# Plot Results
Z = pgp.sess.run(pgp.Z)
m = pgp.sess.run(pgp.m)
plt.figure(figsize=(10,10))
plt.rc('text', usetex=True)
plt.rcParams.update({'font.size': 15})
plt.subplot(2, 1, 1)
plt.plot(X,y,'b+',alpha=1)
plt.xlabel('$x$')
plt.ylabel('$f(x)$')
plt.title('(A)')
plt.legend(['%d traning Data' % N], loc='lower left')
plt.subplot(2, 1, 2)
plt.plot(Z,m, 'ro', alpha=1, markersize=14)
plt.plot(X_star, y_star, 'b-', linewidth=2)
plt.plot(X_star, mean_star, 'r--', linewidth=2)
lower = mean_star - 2.0*np.sqrt(var_star)
upper = mean_star + 2.0*np.sqrt(var_star)
plt.fill_between(X_star.flatten(), lower.flatten(), upper.flatten(), facecolor='orange', alpha=0.5)
plt.xlabel('$x$')
plt.ylabel('$f(x), \overline{f}(x)$')
plt.title('(B)')
plt.tight_layout()
plt.legend(['%d hypothetical data' % M, '$f(x)$', '$\overline{f}(x)$', 'Two standard deviations'], loc='lower left')
plt.savefig('../Fig/OneDimensional.eps', format='eps', dpi=1000)