线性插值 二次插值 拉格郎日插值

#include<iostream>
#include<cmath>
using namespace std;void Linear_interpolation(double *x, double *y, double input);//分段线性插值
void Quadratic_interpolation(double *x,double *y,double u);//分段二次插值
void Lagrange_interpolation(double *x, double *y, double xx);//拉格郎日插值int main()//主函数
{double x[6]={0.0, 0.1, 0.195, 0.3, 0.401, 0.5};double y[6]={0.39894, 0.39695, 0.39142, 0.38138, 0.36812, 0.35206};double u;while(cin>>u){Linear_interpolation(x,y,u); //分段线性插值  Quadratic_interpolation(x,y,u); //分段二次插值Lagrange_interpolation(x,y,u); //拉格郎日插值}  	  }void Linear_interpolation(double *x, double *y, double input)//分段线性插值
{double output;   for (int i=0;i<5;i++)  {  if (x[i] <= input && x[i+1] >= input)  {  output=y[i] +(y[i+1]-y[i])*(input-x[i])/(x[i+1]-x[i]);  break;  }  }  cout<<"Linear_interpolation: "<<output<<endl; 
}void Quadratic_interpolation(double *x,double *y,double u)//分段二次插值
{int i,k=0;  double v;  for(i=0;i<6;i++)  {  if(u<x[1])  {  k=0;  v=y[k]*(u-x[k+1])*(u-x[k+2])/((x[k]-x[k+1])*(x[k]-x[k+2]))+y[k+1]*(u-x[k])*(u-x[k+2])/((x[k+1]-x[k])*(x[k+1]-x[k+2]))+y[k+2]*(u-x[k])*(u-x[k+1])/((x[k+2]-x[k])*(x[k+2]-x[k+1]));  }  if((x[i]<u&&u<=x[i+1])&&(fabs(u-x[i])<=fabs(u-x[i+1])))  {  k=i-1;  v=y[k]*(u-x[k+1])*(u-x[k+2])/((x[k]-x[k+1])*(x[k]-x[k+2]))+y[k+1]*(u-x[k])*(u-x[k+2])/((x[k+1]-x[k])*(x[k+1]-x[k+2]))+y[k+2]*(u-x[k])*(u-x[k+1])/((x[k+2]-x[k])*(x[k+2]-x[k+1]));  }  if ((x[i]<u&&u<=x[i+1])&&fabs(u-x[i])>fabs(u-x[i+1]))  {  k=i;  v=y[k]*(u-x[k+1])*(u-x[k+2])/((x[k]-x[k+1])*(x[k]-x[k+2]))+y[k+1]*(u-x[k])*(u-x[k+2])/((x[k+1]-x[k])*(x[k+1]-x[k+2]))+y[k+2]*(u-x[k])*(u-x[k+1])/((x[k+2]-x[k])*(x[k+2]-x[k+1]));  }  if(u>x[4])  {  k=3;  v=y[k]*(u-x[k+1])*(u-x[k+2])/((x[k]-x[k+1])*(x[k]-x[k+2]))+y[k+1]*(u-x[k])*(u-x[k+2])/((x[k+1]-x[k])*(x[k+1]-x[k+2]))+y[k+2]*(u-x[k])*(u-x[k+1])/((x[k+2]-x[k])*(x[k+2]-x[k+1]));  }  }  cout<<"Quadratic_interpolation: "<<v<<endl;  
}void Lagrange_interpolation(double *x, double *y, double xx)//拉格郎日插值
{int i,j;  double *a, yy=0.000;  a=new double[6];  for(i=0;i< 6;i++)  {  a[i]=y[i];  for(j=0;j< 6;j++)  if(j!=i)  a[i]*=(xx-x[j])/(x[i]-x[j]);  yy+=a[i];  }  delete a;  cout<<"Lagrange_interpolation: "<<yy<<endl;  
}