给定（某条曲线上）多个点，选择合适的函数（可以是一个也可以多个）构造它们的最小二乘拟合，比较拟合函数和原函数的图像及误差。C++

在 C++ 中，可以使用 Eigen 库来实现最小二乘拟合。以下是一个简单的示例代码，它使用多项式函数来拟合一些给定的点：

#include <iostream>
#include <Eigen/Dense>

using namespace Eigen;

int main()
{
    // Define the points to be fitted
    std::vector<double> x = {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
    std::vector<double> y = {1.0, 2.0, 3.0, 4.0, 5.0, 6.0};

    // Define the degree of the polynomial to be fitted
    int degree = 2;

    // Construct the Vandermonde matrix
    MatrixXd A(x.size(), degree + 1);
    for (int i = 0; i < x.size(); i++) {
        for (int j = 0; j < degree + 1; j++) {
            A(i, j) = pow(x[i], j);
        }
    }

    // Construct the right-hand side vector
    VectorXd b(y.size());
    for (int i = 0; i < y.size(); i++) {
        b(i) = y[i];
    }

    // Solve the least squares problem
    VectorXd coeffs = A.bdcSvd(ComputeThinU | ComputeThinV).solve(b);

    // Evaluate the fitted function at some new points
    std::vector<double> newX = {0.5, 1.5, 2.5, 3.5, 4.5};
    std::vector<double> newY(newX.size());
    for (int i = 0; i < newX.size(); i++) {
        double value = 0.0;
        for (int j = 0; j < degree + 1; j++) {
            value += coeffs(j) * pow(newX[i], j);
        }
        newY[i] = value;
    }

    // Print the coefficients of the fitted polynomial
    std::cout << "Coefficients: ";
    for (int i = 0; i < degree + 1; i++) {
        std::cout << coeffs(i) << " ";
    }
    std::cout << std::endl;

    // Plot the original points and the fitted function
    // (not implemented here)

    // Compute the mean squared error between the fitted function and the original points
    double mse = 0.0;
    for (int i = 0; i < x.size(); i++) {
        double value = 0.0;
        for (int j = 0; j < degree + 1; j++) {
            value += coeffs(j) * pow(x[i], j);
        }
        mse += pow(value - y[i], 2.0);
    }
    mse /= x.size();
    std::cout << "Mean squared error: " << mse << std::endl;

    return 0;
}

该示例代码使用多项式函数来拟合一些给定的点，并计算了误差。在实际应用中，可以根据需要选择不同的拟合函数。