c++编写拉格朗日插值

c++编写拉格朗日插值

#include <iostream>
#include <vector>
#include <windows.h>  // 用于设置控制台编码
using namespace std;

double lagrangeInterpolation(vector<double>& x, vector<double>& y, double x_val) {
    double result = 0.0;
    for (size_t i = 0; i < x.size(); i++) {
        double term = y[i];
        for (size_t j = 0; j < x.size(); j++) {
            if (j != i) {
                term *= (x_val - x[j]) / (x[i] - x[j]);
            }
        }
        result += term;
    }
    return result;
}

int main() {
    SetConsoleOutputCP(CP_UTF8);  // 设置控制台为 UTF-8 编码
    
    vector<double> x = {0, 1, 2, 3};
    vector<double> y = {1, 2, 0, 4};
    
    cout << "已知数据点：" << endl;
    for (size_t i = 0; i < x.size(); i++) {
        cout << "(" << x[i] << ", " << y[i] << ")" << endl;
    }
    
    double x_test = 1.5;
    double y_result = lagrangeInterpolation(x, y, x_test);
    
    cout << "\n插值结果：" << endl;
    cout << "当x = " << x_test << "时，y = " << y_result << endl;
    
    return 0;
}