C++ 多变量梯度下降法代码

以下是一个简单的 C++ 多变量梯度下降法的代码示例：

#include <iostream>
#include <vector>

using namespace std;

double learning_rate = 0.01; // 学习率
int num_iterations = 1000; // 迭代次数

// 计算损失函数
double compute_cost(vector<double>& x, vector<double>& y, double theta0, double theta1) {
    double cost = 0.0;
    int m = x.size();
    for (int i = 0; i < m; i++) {
        double h = theta0 + theta1 * x[i];
        cost += (h - y[i]) * (h - y[i]);
    }
    cost /= (2 * m);
    return cost;
}

// 梯度下降法更新参数
void gradient_descent(vector<double>& x, vector<double>& y, double& theta0, double& theta1) {
    int m = x.size();
    double temp0 = 0.0, temp1 = 0.0;
    for (int i = 0; i < m; i++) {
        double h = theta0 + theta1 * x[i];
        temp0 += (h - y[i]);
        temp1 += (h - y[i]) * x[i];
    }
    theta0 -= learning_rate * temp0 / m;
    theta1 -= learning_rate * temp1 / m;
}

int main() {
    vector<double> x = {1.0, 2.0, 3.0, 4.0, 5.0};
    vector<double> y = {2.0, 4.0, 6.0, 8.0, 10.0};
    double theta0 = 0.0, theta1 = 0.0;
    for (int i = 0; i < num_iterations; i++) {
        double cost = compute_cost(x, y, theta0, theta1);
        gradient_descent(x, y, theta0, theta1);
        cout << "Iteration " << i << ", cost = " << cost << ", theta0 = " << theta0 << ", theta1 = " << theta1 << endl;
    }
    return 0;
}

该示例代码实现了一个简单的线性回归模型，使用梯度下降法来更新模型参数，以最小化损失函数。其中 `x` 和 `y` 分别表示输入和输出数据，`theta0` 和 `theta1` 表示模型参数。在每次迭代中，都会计算当前的损失函数值，并更新模型参数。