加权三次多项式拟合C++代码实现

以下是加权三次多项式拟合的C++代码实现，其中使用了Eigen库进行矩阵计算：

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

using namespace Eigen;

int main()
{
    // 输入数据
    int n = 5; // 数据点个数
    MatrixXd X(n, 4);
    VectorXd y(n);
    VectorXd w(n);
    X << 1, 1, 1, 1,
         2, 4, 8, 16,
         3, 9, 27, 81,
         4, 16, 64, 256,
         5, 25, 125, 625;
    y << 1, 2, 3, 4, 5;
    w << 1, 2, 3, 4, 5;

    // 计算加权三次多项式系数
    MatrixXd A(n, 4);
    A << w.array().sqrt().matrix().asDiagonal() * X;
    VectorXd b = w.array().sqrt() * y;
    Vector4d coef = A.colPivHouseholderQr().solve(b);

    // 输出结果
    std::cout << "Coefficients: " << coef.transpose() << std::endl;

    return 0;
}

相关问题

加权多项式拟合C++代码实现

以下是加权多项式拟合的C++代码实现，包括数据读取、计算多项式系数和输出结果三个部分：

1.数据读取部分：

#include <iostream>
#include <fstream>
#include <vector>

using namespace std;

// 读取数据文件
void readData(string filename, vector<double>& x, vector<double>& y, vector<double>& w) {
    ifstream fin(filename);
    double xi, yi, wi;
    while (fin >> xi >> yi >> wi) {
        x.push_back(xi);
        y.push_back(yi);
        w.push_back(wi);
    }
    fin.close();}

2.计算多项式系数部分：

#include <Eigen/Dense>
#include <vector>

using namespace Eigen;
using namespace std;

// 计算多项式系数
VectorXd polyfit(vector<double>& x, vector<double>& y, vector<double>& w, int order) {
    int n = x.size();
    MatrixXd A(n, order + 1);
    VectorXd b(n);
    VectorXd wv(n);
    for (int i = 0; i < n; i++) {
        wv(i) = sqrt(w[i]);
        for (int j = 0; j <= order; j++) {
            A(i, j) = pow(x[i], j) * wv(i);
        }
        b(i) = y[i] * wv(i);
    }
    VectorXd coeffs = A.colPivHouseholderQr().solve(b);
    return coeffs;
}

3.输出结果部分：

#include <iostream>
#include <vector>

using namespace std;

// 输出结果
void printResult(VectorXd coeffs) {
    int n = coeffs.size() - 1;
    cout << "The polynomial is: ";
    for (int i = n; i >= 0; i--) {
        cout << coeffs(n - i) << "x^" << i;
        if (i > 0) {
            cout << " + ";
        }
    }
    cout << endl;
}

完整代码如下：

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

using namespace Eigen;
using namespace std;

// 读取数据文件
void readData(string filename, vector<double>& x, vector<double>& y, vector<double>& w) {
    ifstream fin(filename);
    double xi, yi, wi;
    while (fin >> xi >> yi >> wi) {
        x.push_back(xi);
        y.push_back(yi);
        w.push_back(wi);
    }
    fin.close();
}

// 计算多项式系数
VectorXd polyfit(vector<double>& x, vector<double>& y, vector<double>& w, int order) {
    int n = x.size();
    MatrixXd A(n, order + 1);
    VectorXd b(n);
    VectorXd wv(n);
    for (int i = 0; i < n; i++) {
        wv(i) = sqrt(w[i]);
        for (int j = 0; j <= order; j++) {
            A(i, j) = pow(x[i], j) * wv(i);
        }
        b(i) = y[i] * wv(i);
    }
    VectorXd coeffs = A.colPivHouseholderQr().solve(b);
    return coeffs;
}

// 输出结果
void printResult(VectorXd coeffs) {
    int n = coeffs.size() - 1;
    cout << "The polynomial is: ";
    for (int i = n; i >= 0; i--) {
        cout << coeffs(n - i) << "x^" << i;
        if (i > 0) {
            cout << " + ";
        }
    }
    cout << endl;
}

int main() {
    vector<double> x, y, w;
    readData("data.txt", x, y, w);
    VectorXd coeffs = polyfit(x, y, w, 2);
    printResult(coeffs);
    return 0;
}