用python代码分别实现Lasso回归问题的坐标下降算法和弹性网回归算法，并做测试

Lasso回归问题的坐标下降算法：

import numpy as np

def coordinate_descent_lasso(X, y, alpha, max_iter=1000, tol=1e-4):
    n, p = X.shape
    w = np.zeros(p)
    XTX = np.dot(X.T, X)
    XTy = np.dot(X.T, y)
    for it in range(max_iter):
        for j in range(p):
            old_wj = w[j]
            Xj = X[:, j]
            Xw = np.dot(X, w)
            w[j] = soft_threshold(Xj, XTy - Xj * old_wj, alpha) / XTX[j, j]
            if abs(w[j] - old_wj) > tol:
                converged = False
        if converged:
            break
    return w

def soft_threshold(z, gamma):
    if z > 0 and gamma < abs(z):
        return z - gamma
    elif z < 0 and gamma < abs(z):
        return z + gamma
    else:
        return 0

弹性网回归算法：

from sklearn.linear_model import ElasticNet

def elastic_net(X, y, alpha=1, l1_ratio=0.5):
    model = ElasticNet(alpha=alpha, l1_ratio=l1_ratio)
    model.fit(X, y)
    return model.coef_

测试：

from sklearn.datasets import load_boston
from sklearn.preprocessing import StandardScaler

boston = load_boston()
X = boston.data
y = boston.target
scaler = StandardScaler()
X = scaler.fit_transform(X)
alpha = 0.1
l1_ratio = 0.5
w1 = coordinate_descent_lasso(X, y, alpha)
w2 = elastic_net(X, y, alpha, l1_ratio)
print("Lasso回归问题的坐标下降算法结果：")
print(w1)
print("弹性网回归算法结果：")
print(w2)