#include"TH1D.h"
#include "TF1.h"
double X[100];
double Y[100];
int n=10; //i nodi sono n+1
double fteorica(double x)
{ 
	double y=(x*x*x)*cos(x);
	return y;
}
double Lagrange(double x, int i)
{
	double y=1.;
	for(int j=0; j<n+1; j++)
	{
		if(j==i) continue;
		y=y*(x-X[j])/(X[i]-X[j]);
	}
 	return y;
}
double ginterpol(double x)
{
	double y=0;
	for(int j=0;j<n+1; j++)
	{
		y=y+Y[j]*Lagrange(x,j);
	}
 	return y;
}

void interpolazione ()
{

	
	double a=-10.;
	double b=10.;
	TF1 *ptfteorica= new TF1("tfteorica","fteorica(x)",a,b);
	ptfteorica->SetLineColor(kRed);
	ptfteorica->Draw();
	X[0]=a;
	X[n]=b;
	double passo=(X[n]-X[0])/n;
	cout<< "al passo i=0, X="<<X[0]<<endl;
	Y[0]=fteorica(X[0])	;
		cout<< "al passo i=0, Y="<<Y[0]<<endl;  
	for(int i=1; i<n+1;i++)
	{
		X[i]=X[i-1]+passo;
		cout<< "al passo i="<<i<<" ,X="<<X[i]<<endl; 
		Y[i]=fteorica(X[i])	;
		cout<< "al passo i="<<i<<" ,Y="<<Y[i]<<endl; 
	}
	TF1 *pfinterpol= new TF1("finterpol","ginterpol(x)",a,b);
	pfinterpol->SetLineColor(kBlue);
	pfinterpol->SetLineStyle(2);
	pfinterpol->Draw("same");
	TF1 *resto= new TF1("rest","fteorica(x)-ginterpol(x)",a,b);
		TCanvas *c2=new TCanvas("c2","c2", 800,600);
	resto->Draw();
	
	
	
		
}