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拉格朗日插值法
2022-07-06 04:16:00 【Python ml】
#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;
}
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