拉格朗日插值法

#include <vector>
#include <iostream>

using namespace std;

void print(vector<double> s)
{
    
    for(double x:s)
    {
    
        cout<<x<<" ";
    }
    cout<<endl;
}

vector<double> mul(vector<double> a,vector<double> b)    //多项式乘法
{
    
    int n=a.size(), m=b.size();
    vector<double> s(n+m-1,0);
    for(int i=0;i<n;++i)
    {
    
        for(int j=0;j<m;++j)
        {
    
            s[i+j]+=a[i]*b[j];
        }
    }
    return s;
}

vector<double> add(vector<double> a,vector<double> b)  
{
    
    int n=a.size(), m=b.size();
    vector<double> s(max(n,m),0);
    for(int i=0;i<n;++i){
    
        s[i]+=a[i];
    }
    for(int i=0;i<m;++i){
    
        s[i]+=b[i];
    }
    return s;
}

vector<double>Lagrange(vector<vector<double>> Point){
    
    int n=Point.size()-1;            //插值ans为n次方
    if(n==-1){
    
        cout<<"错误"<<endl;
    }
    vector<double> ans(n,0);
    for(int k=0;k<=n;++k)
    {
    
        double Poly_k_const=Point[k][1];
        vector<double> Poly_k={
    1};
        for(int i=0;i<=n;++i)
        {
    
            if(i==k) continue;
            Poly_k=mul(Poly_k,{
    -Point[i][0],1});      //分子连乘(x-Point[i][0])
            Poly_k_const/=(Point[k][0]-Point[i][0]);
        }
        for(int i=0;i<Poly_k.size();++i){
    
            Poly_k[i]*=Poly_k_const;
        }
        ans=add(ans,Poly_k);
    }
    return ans;
}