lagrange1.cpp

这是计算方法上的所有算法

#include<iostream>
#include<conio.h>
#include<iomanip>
using namespace std;
#define N 4

int checkvalid(double x[],int n)
{
	int i,j,flag=1;
	for(i=0;i<n;i++)
	{
		for(j=i+1;j<n;j++)
			if(x[i]==x[j])
			{
				flag=-1;								
			}			
	}	
		return(flag);
}
double Lagrange(double x[],double y[],double varx,int n)
{
	cout<<"Ln(x)="<<endl;
	int i,j,k;
	double v=0;
	for(i=0;i<=n;i++)
	{	double l=1,temp=1;
		for(j=0;j<=n;j++)
		{
		if(j==i) continue;
		temp=temp*(1/(x[i]-x[j]));
		l=l*(varx-x[j]);		
		}
		
		cout<<setiosflags(ios_base::fixed)<<setiosflags(ios_base::left)
			<<setw(6)<<"  "<< setprecision(6)<<l*temp;
		for(k=0;k<j;k++)
		{
			if(k==i) continue;
			cout<<"*(x-"<<x[k]<<")";
		}						
		v=v+l*y[i]*temp;
		if(i==n-1)
			continue;
		else
		cout<<"+"<<endl;
	}	
	return (v);
}
void main()
{
	double x[N+1]={0.4,0.55,0.80,0.9,1};
	double y[N+1]={0.41075,0.57815,0.88811,1.02652,1.17520};
	double varx=0.5;
	int checkvalid(double x[],int n);
	double Lagrange(double x[],double y[],double varx,int n);
	if(checkvalid(x,N)==1)
		cout<<setiosflags(ios_base::fixed)<<"\n\n插值结果:P"<<"("<<varx<<")="<<setprecision(6)<<Lagrange(x,y,varx,N);            
	else
		cout<<"输入的插值节点的"<<x<<"值必须互异!";          
	getch();
}