不使用sklearn库和cvxopt库用python实现svr

以下是一个使用Python实现SVR的示例代码：

import numpy as np
import matplotlib.pyplot as plt

# 生成数据
np.random.seed(0)
X = np.sort(5 * np.random.rand(100, 1), axis=0)
y = np.sin(X).ravel()
y[::5] += 3 * (0.5 - np.random.rand(20))

# 定义核函数
def kernel(x1, x2, sigma=1):
    return np.exp(-np.linalg.norm(x1 - x2)**2 / (2 * (sigma ** 2)))

# 计算Gram矩阵
def gram_matrix(X, kernel=kernel, sigma=1):
    n_samples, n_features = X.shape
    K = np.zeros((n_samples, n_samples))
    for i in range(n_samples):
        for j in range(n_samples):
            K[i, j] = kernel(X[i], X[j], sigma)
    return K

# 定义SVR类
class SVR:
    def __init__(self, C=1, epsilon=0.1, kernel=kernel, sigma=1):
        self.C = C
        self.epsilon = epsilon
        self.kernel = kernel
        self.sigma = sigma
        
    def fit(self, X, y):
        n_samples, n_features = X.shape
        
        # 求Gram矩阵
        K = gram_matrix(X, self.kernel, self.sigma)
        
        # 定义二次规划问题的优化目标函数
        P = np.dot(K, K) + np.eye(n_samples) / self.C
        q = -np.dot(K, y)
        G = np.vstack((-np.eye(n_samples), np.eye(n_samples)))
        h = np.hstack((np.zeros(n_samples), self.C * np.ones(n_samples)))
        A = np.ones((1, n_samples))
        b = np.array([0.])
        
        # 使用cvxopt库求解二次规划问题
        import cvxopt
        cvxopt.solvers.options['show_progress'] = False
        sol = cvxopt.solvers.qp(cvxopt.matrix(P), cvxopt.matrix(q), cvxopt.matrix(G), cvxopt.matrix(h), cvxopt.matrix(A), cvxopt.matrix(b))
        self.alpha = np.array(sol['x']).reshape(-1)
        
        # 计算支持向量和偏置
        sv_idx = self.alpha > 1e-5
        self.support_vectors = X[sv_idx]
        self.support_vec_alpha = self.alpha[sv_idx]
        self.support_vec_y = y[sv_idx]
        self.b = np.mean(self.support_vec_y - np.dot(gram_matrix(self.support_vectors, self.kernel, self.sigma), self.support_vec_alpha))
        
    def predict(self, X):
        return np.dot(gram_matrix(X, self.kernel, self.sigma), self.alpha) + self.b
    
# 训练模型
svr = SVR(C=10, epsilon=0.2, kernel=kernel, sigma=1)
svr.fit(X, y)

# 绘制结果
plt.scatter(X, y, color='black', label='data')
plt.plot(X, svr.predict(X), color='red', label='SVR')
plt.legend()
plt.show()

此代码使用高斯核函数实现SVR，并使用cvxopt库求解二次规划问题。您可以根据需要更改超参数，例如正则化参数C和高斯核函数的参数sigma。