//
//  lagrange.cpp
//  
//
//  Created by stefania spagnolo on 08/11/21.
//

#include "lagrange.hpp"

void drawPiFunction(int n=10)
{
    TH2F* hb = new TH2F("hbox","",100,0.,double(n+0.5),100,-100.,100.);
    TF1 * pifp1=new TF1("pip1",pi_n1,0.,double(n+1),1);
    pifp1->SetParameter(0,double(n+1));
    TF1 * pifm1=new TF1("pim1",pi_n1,0.,double(n-1),1);
    pifm1->SetParameter(0,double(n-1));
    TF1 * pif=new TF1("pi",pi_n1,0.,double(n-1),1);
    pif->SetParameter(0,double(n));
    
   //hb->Draw();
    //pif->Draw("same");
    TCanvas* c1 = new TCanvas("c","c",800,600);
//    c1->Divide(2,2);
//    c1->cd(1);
    //pif->Draw();
    //pif->DrawF1(1.,double(n-2));
    pif->DrawF1(2.,double(n-3));
    //pif->DrawF1(3.,double(n-4));

}

double pi_n1(double* t, double* n1)
{
    // pi_{n+1} = t(t-1)(t-2)...(t-n)
    double result = 1.;
    for (int i=0; i<n1[0]; ++i)
    {
        result = result*(t[0]-(double)i);
    }
    
    return result;
}