Nt0 = 36 i0 = np.random.randint(0, len(E0), size=Nt0) T0 = np.array([E0[i] for i in i0]) X0, Y0 = np.split(T0, 2, axis=1) # Level 1 training set Nt1 = 10 i1 = np.random.choice(i0, size=Nt1) T1 = np.array([E1[i] for i in i1]) X1, Y1 = np.split(T1, 2, axis=1) # Test set Xtest = matrix.Col(E1[:, 0]) # Optimize level 1 m0 = ordinary.optimize(X0, Y0) # Optimize level 2 mu0, C0 = ordinary.predict(m0, X1, full_cov=True) m1 = nargp.optimize(mu0, X1, Y1) # Predict level 1 mu0, C0 = ordinary.predict(m0, Xtest, full_cov=True) S0 = np.sqrt(np.diag(C0)) # Predict Level 2 mu1, C1 = nargp.predict(m1, mu0, C0, Xtest) S1 = np.sqrt(C1) # Row vectors for plotting mu0, S0 = np.ravel(mu0), np.ravel(S0)
# Dimensions of system
dim = 3
active_dimensions=np.arange(0, dim)
f = open("rmse.dat", "a")
for N1, N2 in zip(Nt1, Nt2):
# Level 1 training set
train, test = data_sampler.smart_random(E1, N1, n_test=None)
X1, Y1 = np.split(E1[train], [dim], axis=1)
# Train level 1
k1 = GPy.kern.RBF(dim, ARD=True)
m1 = ordinary.optimize(X1, Y1, k1, normalize=True, restarts=12)
mu1, v1 = ordinary.predict(m1, Xtest, full_cov=True)
# Level 2 training set
train2, test2 = data_sampler.smart_random2(E2, N2, train, test)
X2, Y2 = np.split(E2[train2], [dim], axis=1)
# Predict level 1 at X2
mu1_, v1_ = ordinary.predict(m1, X2, full_cov=True)
# Train level 2
XX = np.hstack((X2, mu1_))
k2 = GPy.kern.RBF(1, active_dims = [dim]) * GPy.kern.RBF(dim, active_dims = active_dimensions, ARD = True) \
+ GPy.kern.RBF(dim, active_dims = active_dimensions, ARD = True)
m2 = GPy.models.GPRegression(X=XX, Y=Y2, kernel=k2, normalizer=True)
m2.optimize(max_iters=1000)
X1 = Xtrain[idx[0:N1], :]
Y1 = np.array([my_high(*i) for i in X1])[:, np.newaxis]
lb = np.array([-1.5, -0.5])
ub = np.array([0.9, 0.75])
x1 = np.linspace(lb[0], ub[0], 50)
x2 = np.linspace(lb[1], ub[1], 50)
tmp = np.random.rand(1000,2)
Xtest = scale_range(tmp,ub,lb)
active_dimensions = np.arange(0,dim)
# Ordinary GP
kernel = GPy.kern.RBF(dim, ARD=True)
model = ordinary.optimize(X1, Y1, kernel, normalize=False)
mu, v = ordinary.predict(model, Xtest)
# Calculate error
Exact = np.array([my_high(*i) for i in Xtest])
Exact = Exact[:, np.newaxis]
ogp_error = np.linalg.norm(Exact - mu)/np.linalg.norm(Exact)
print("error: ", ogp_error)
# Exact plot
X, Y = np.meshgrid(x1, x2)
Exactplot = ml.griddata(Xtest[:,0], Xtest[:,1], Exact[:, 0], X, Y, interp='linear')
fig = plt.figure(1)
ax1 = fig.add_subplot(111, projection='3d')
ax1.plot_surface(X, Y, Exactplot, color = '#377eb8', rstride=2, cstride=2,
linewidth=0, antialiased=True, shade = True, alpha = 0.6)
import GPy
import numpy as np
from ARGP import ordinary
from ARGP import data_sampler
E = np.loadtxt("surfaces/ccsd-t-5z.dat", delimiter=',', skiprows=1)
E[:, -1] += 76.203896662997
# Test set
Xtest = E[:, :-1]
dim = len(Xtest.T)
# Training set size
Nt = 120
# Sample training set
train, test = data_sampler.smart_random(E, Nt, n_test=None)
T = E[train]
X1, Y1 = np.split(T, [dim], axis=1)
# Ordinary GP regression
kernel = GPy.kern.RBF(dim, ARD=True)
model = ordinary.optimize(X1, Y1, kernel, normalize=True, restarts=10)
mu, v = ordinary.predict(model, Xtest)
# Calculate error
exact = E[:, -1].reshape(-1, 1)
error = 1000 * np.sqrt(np.mean((mu - exact)**2))
print("Test error: {:>5.3} mEh".format(error))
np.random.seed(0)
# Load ab initio surface
E = np.loadtxt("surfaces/mrci-pcv5z.tab")
E[:, 1] += 109.15851906
# Training set
Nt = 10
index = np.random.randint(0, len(E), size=Nt)
X, Y = np.split(E[index], 2, axis=1)
# Test set
Xtest = E[:, 0].reshape(-1, 1)
# Train ordinary model
m = ordinary.optimize(X, Y, normalize=True)
mu, C = m.predict(Xtest, full_cov=True)
S = np.sqrt(np.diag(C))
mu, S = np.ravel(mu), np.ravel(S)
rmse = 1000 * np.sqrt(((mu - E[:, 1])**2).mean())
print("Prediction Error: {:>9.4f} mEh".format(rmse))
if __name__ == '__main__':
# Size of confidence interval
ns = 3
# Plotting
plt.xlim(0.8, 2.35)
plt.ylim(-0.4, 0.6)