帮我用python写svr算法实现回归预测，要求不能使用python中的相关库

好，我们来实现一个简单的SVR算法，以下是代码实现：

import numpy as np

class SVR:
    def __init__(self, C=1, epsilon=0.1, kernel='linear', gamma=None):
        self.C = C
        self.epsilon = epsilon
        self.kernel = kernel
        self.gamma = gamma
    
    def fit(self, X, y):
        n_samples, n_features = X.shape
        
        # Kernel matrix
        if self.kernel == 'linear':
            kernel_matrix = np.dot(X, X.T)
        elif self.kernel == 'rbf':
            if self.gamma is None:
                self.gamma = 1 / n_features
            kernel_matrix = np.zeros((n_samples, n_samples))
            for i in range(n_samples):
                for j in range(n_samples):
                    kernel_matrix[i, j] = np.exp(-self.gamma * np.linalg.norm(X[i] - X[j]) ** 2)
        else:
            raise ValueError('Unsupported kernel type')
        
        # Quadratic programming problem
        P = np.vstack((np.hstack((kernel_matrix, -kernel_matrix)), np.hstack((-kernel_matrix, kernel_matrix))))
        q = np.hstack((self.epsilon - y, self.epsilon + y))
        G = np.vstack((np.eye(2 * n_samples), -np.eye(2 * n_samples)))
        h = np.hstack((self.C * np.ones(2 * n_samples), np.zeros(2 * n_samples)))
        sol = self.quadprog(P, q, G, h)
        
        # Support vectors
        sv_idx = np.where(np.abs(sol) > 1e-5)[0]
        self.support_vectors = X[sv_idx]
        self.dual_coef = sol[sv_idx]
        self.intercept = np.mean(y[sv_idx] - np.dot(kernel_matrix[sv_idx, :], self.dual_coef))
    
    def predict(self, X):
        if self.kernel == 'linear':
            kernel_matrix = np.dot(X, self.support_vectors.T)
        elif self.kernel == 'rbf':
            kernel_matrix = np.zeros((X.shape[0], self.support_vectors.shape[0]))
            for i in range(X.shape[0]):
                for j in range(self.support_vectors.shape[0]):
                    kernel_matrix[i, j] = np.exp(-self.gamma * np.linalg.norm(X[i] - self.support_vectors[j]) ** 2)
        else:
            raise ValueError('Unsupported kernel type')
        
        return np.dot(kernel_matrix, self.dual_coef) + self.intercept
    
    def quadprog(self, P, q, G, h):
        # Solve quadratic programming problem using active set method
        n_samples = P.shape[0]
        active = np.zeros(n_samples, dtype=bool)
        alpha = np.zeros(n_samples)
        obj = np.inf
        
        while True:
            # Solve subproblem
            G_active = G[active, :]
            P_active = P[:, active][active, :]
            q_active = q[active]
            h_active = h[active]
            try:
                alpha_active = np.linalg.solve(P_active, q_active)
            except np.linalg.LinAlgError:
                alpha_active = np.zeros(G_active.shape[0])
            
            # Compute optimality
            r = q_active - np.dot(P_active, alpha_active)
            if np.all(r <= self.epsilon) and np.all(h_active >= 0):
                # Optimal solution found
                obj = np.dot(alpha_active, np.dot(P_active, alpha_active)) - np.sum(alpha_active)
                alpha[active] = alpha_active
                break
            
            # Compute maximum feasible direction
            d = np.zeros(n_samples)
            d[active] = np.dot(np.linalg.inv(P_active), G_active.T.dot(np.maximum(r, 0)))
            i = np.argmax(np.abs(d * (~active)))
            if d[i] >= 0:
                # Unbounded objective function
                break
            
            # Add i to active set
            active[i] = True
        
        return alpha

代码中实现了线性核和RBF核的SVR算法。其中，fit方法用来训练模型，predict方法用来进行预测。quadprog方法实现了求解二次规划问题的算法，用于训练模型时求解对偶问题。