Polynomial 回归 C++ 代码

以下是一个简单的多项式回归的 C++ 代码示例：

#include <iostream>
#include <vector>
#include <cmath>

using namespace std;

// 计算多项式回归系数
vector<double> polyfit(vector<double> x, vector<double> y, int degree)
{
    int n = x.size();
    vector<double> coeffs(degree + 1, 0);
    vector<double> sx(2 * degree + 1, 0);
    vector<double> sy(degree + 1, 0);

    for (int i = 0; i < n; ++i)
    {
        double xi = x[i], yi = y[i];
        for (int j = 0; j <= degree; ++j)
        {
            sx[j] += pow(xi, j);
        }
        for (int j = 0; j <= degree; ++j)
        {
            sy[j] += yi * pow(xi, j);
        }
    }

    for (int i = 0; i <= degree; ++i)
    {
        for (int j = 0; j <= degree; ++j)
        {
            coeffs[i] += pow(-1, i + j) * sy[j] * sx[i + j];
        }
        coeffs[i] /= pow(x.size(), 2 * degree - i);
    }

    return coeffs;
}

int main()
{
    vector<double> x = { 1, 2, 3, 4, 5 };
    vector<double> y = { 1.2, 3.5, 4.2, 4.8, 5.1 };
    int degree = 2;

    vector<double> coeffs = polyfit(x, y, degree);

    cout << "The coefficients are: ";
    for (int i = 0; i <= degree; ++i)
    {
        cout << coeffs[i] << " ";
    }
    cout << endl;

    return 0;
}

这个程序使用向量表示多项式回归的输入数据。在 `polyfit` 函数中，我们首先分配了一些向量来存储计算所需的中间结果。然后，我们使用两个循环来计算 $s_{x,j}$ 和 $s_{y,j}$。最后，我们使用第三个循环计算回归系数。