# Exponential correlation model are used.
# %%
regression_model = ConstantRegression()
kernel = Matern(nu=0.5)
from UQpy.utilities.MinimizeOptimizer import MinimizeOptimizer
optimizer = MinimizeOptimizer(method="L-BFGS-B")
K = GaussianProcessRegression(regression_model=regression_model,
optimizer=optimizer,
kernel=kernel,
optimizations_number=20,
hyperparameters=[1, 1, 0.1])
K.fit(samples=x.samples, values=rmodel.qoi_list)
print(K.hyperparameters)
# %% md
#
# This plot shows the actual model which is used to evaluate the samples to identify the function values.
# %%
num = 25
x1 = np.linspace(0, 1, num)
x2 = np.linspace(0, 1, num)
x1g, x2g = np.meshgrid(x1, x2)
x1gv, x2gv = x1g.reshape(x1g.size, 1), x2g.reshape(x2g.size, 1)
# %%
gpr2 = GaussianProcessRegression(kernel=kernel2,
hyperparameters=[1, 1, 0.1],
optimizer=optimizer2,
optimizations_number=10,
noise=True,
regression_model=LinearRegression())
# %% md
#
# Call the 'fit' method to train the surrogate model (GPR).
# %%
gpr2.fit(X_train, y_train)
# %% md
#
# The maximum likelihood estimates of the hyperparameters are as follows:
# %%
print(gpr2.hyperparameters)
print('Length Scale: ', gpr2.hyperparameters[0])
print('Process Variance: ', gpr2.hyperparameters[1])
print('Noise Variance: ', gpr2.hyperparameters[2])
# %% md
#
# %%
gpr1 = GaussianProcessRegression(kernel=kernel1,
hyperparameters=[10**(-3), 10**(-2)],
optimizer=optimizer1,
optimizations_number=10,
noise=False,
regression_model=LinearRegression())
# %% md
#
# Call the 'fit' method to train the surrogate model (GPR).
# %%
gpr1.fit(X_train, y_train)
# %% md
#
# The maximum likelihood estimates of the hyperparameters are as follows:
# %%
gpr1.hyperparameters
print('Length Scale: ', gpr1.hyperparameters[0])
print('Process Variance: ', gpr1.hyperparameters[1])
# %% md
#
# Use 'predict' method to compute surrogate prediction at the test samples. The attribute 'return_std' is a boolean
kernel=kernel3,
hyperparameters=[10**(-3), 10**(-2), 10**(-10)],
optimizer=optimizer3,
optimizations_number=10,
optimize_constraints=cons,
bounds=bounds_3,
noise=True,
regression_model=QuadraticRegression())
# %% md
#
# Call the 'fit' method to train the surrogate model (GPR).
# %%
gpr3.fit(X_train, y_train)
# %% md
#
# The maximum likelihood estimates of the hyperparameters are as follows:
# %%
print(gpr3.hyperparameters)
print('Length Scale: ', gpr3.hyperparameters[0])
print('Process Variance: ', gpr3.hyperparameters[1])
print('Noise Variance: ', gpr3.hyperparameters[2])
# %% md
#