ShuaiGuo16

def Test_2D(X):
    """2D Test Function"""
    
    y = (1-X[:,0])**2 + 100*(X[:,1]-X[:,0]**2)**2
    
    return y

ShuaiGuo16

# Training data
sample_num = 25
lb, ub = np.array([-2, -1]), np.array([2, 3])
X_train = (ub-lb)*lhs(2, samples=sample_num) + lb
y_train = Test_2D(X_train).reshape(-1,1)

# Test data
X1 = np.linspace(-2, 2, 20)
X2 = np.linspace(-1, 3, 20)
X1, X2 = np.meshgrid(X1, X2)

ShuaiGuo16

def Test_1D(X):
    """1D Test Function"""
    
    y = (X*6-2)**2*np.sin(X*12-4)
    
    return y

# Training data
X_train = np.array([0.0, 0.1, 0.2, 0.4, 0.5, 0.6, 0.8, 1], ndmin=2).T
y_train = Test_1D(X_train)

ShuaiGuo16

    def score(self, X_test, y_test):
        """Calculate root mean squared error
        
        Input
        -----
        X_test: test set, array of shape (n_samples, n_features)
        y_test: test labels, array of shape (n_samples, )
        
        Output
        ------

ShuaiGuo16

    def predict(self, X_test):
        """GP model predicting
        
        Input
        -----
        X_test: test set, array of shape (n_samples, n_features)
        
        Output
        ------
        f: GP predictions

ShuaiGuo16

    def fit(self, X, y):
        """GP model training
        
        Input
        -----
        X: 2D array of shape (n_samples, n_features)
        y: 2D array of shape (n_samples, 1)
        """
        
        self.X, self.y = X, y

ShuaiGuo16

    def Neglikelihood(self, theta):
        """Negative likelihood function
        
        Input
        -----
        theta: array, logarithm of the correlation legnths for different dimensions
        
        Output
        ------
        LnLike: likelihood value"""

ShuaiGuo16

    def Corr(self, X1, X2, theta):
        """Construct the correlation matrix between X1 and X2
        
        Input
        -----
        X1, X2: 2D arrays, (n_samples, n_features)
        theta: array, correlation legnths for different dimensions
        
        Output
        ------

ShuaiGuo16

class GaussianProcess:
    """A Gaussian Process class for creating and exploiting  
    a Gaussian Process model"""
    
    def __init__(self, n_restarts, optimizer):
        """Initialize a Gaussian Process model
        
        Input
        ------
        n_restarts: number of restarts of the local optimizer

ShuaiGuo16

# import all packages and set plots to be embedded inline
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import minimize
from scipy.optimize import Bounds
from pyDOE import lhs
from sklearn.preprocessing import MinMaxScaler
from sklearn.pipeline import Pipeline

%matplotlib inline