// -------- ROOT Macro chi2PDF -------------------
// Description: plot chi2 distribution
// Author:      G. Quast, Dec. 2013
// last modified: 
//
// dependencies: ROOT 
//------------------------------------------------

#ifndef __CINT__
#include <TF1.h>
#include <TCanvas.h>
#endif

 Double_t chi2(Double_t *x, Double_t *par)
 // chi2 pdf
{
  return ROOT::Math::chisquared_pdf(x[0],par[0],par[1]);
}

Double_t chi2F(Double_t *x, Double_t *par)
//chi2 cumulative distribution function
{ 
  return ROOT::Math::chisquared_cdf(x[0],par[0],par[1]);
}

Double_t chi2P(Double_t *x, Double_t *par)
//chi2 probability
{ 
  return 1.-ROOT::Math::chisquared_cdf(x[0],par[0],par[1]);
}

 Double_t chi2n(Double_t *x, Double_t *par)
 // normalized chi2 pdf (chi2/ndf)
{
  return ROOT::Math::chisquared_pdf(x[0]*par[0],par[0],par[1])*par[0];
}

Double_t chi2Fn(Double_t *x, Double_t *par)
//normalized chi2 cumulative distribution function
{ 
  return ROOT::Math::chisquared_cdf(x[0]*par[0],par[0],par[1]);
}

Double_t chi2Pn(Double_t *x, Double_t *par)
//normalized chi2, probability
{ 
  return 1.-ROOT::Math::chisquared_cdf(x[0]*par[0],par[0],par[1]);
}

void chi2Prob() {

  TF1 *Fchi2  =    new TF1("chi2",chi2, 0.,12.,200);
  TF1 *Fchi2F  =    new TF1("chi2F",chi2F, 0.,25.,200);
  TF1 *Fchi2P  =    new TF1("chi2P",chi2P, 0.,25.,200);
  TF1 *Fchi2n  =    new TF1("chi2n",chi2n, 0.,4.,200);
  TF1 *Fchi2Fn  =    new TF1("chi2Fn",chi2Fn, 0.,5.,200);
  TF1 *Fchi2Pn  =    new TF1("chi2Pn",chi2Pn, 0.,5.,200);

// make a white canvas without borders
TCanvas *c1 = new TCanvas("c1", "c1", 0, 0, 700, 500);
   c1->SetFillColor(0);
   c1->SetBorderMode(0);
   c1->SetBorderSize(0);
   c1->SetGridx();
   c1->SetGridy();
   c1->SetFrameBorderMode(0);
   c1->cd();  
gStyle->SetOptTitle(0);

// plot one of these functions for different n_f
//TF1 *Func = Fchi2;
TF1 *Func = Fchi2P;
Func->SetParameter(1,0);
Func->SetParameter(0,2);
Func->SetLineColor(kWhite);
Func->SetTitle("#chi^{2} Verteilung;#chi^{2}; P-value");
Func->DrawCopy();
 
TLegend* legend = new TLegend(0.79, 0.28, 0.87, 0.88);
char title[20];
TObject* copied; 

int ndf=1;
 for (int ils=1; ils<4; ils++) { 
   for (int ilc=1; ilc<8; ilc++) {
     Func->SetLineStyle(ils); 
     Func->SetLineColor(ilc);
     ndf=ndf+1;
     Func->SetParameter(0,ndf);
     Func->DrawCopy("same");
     sprintf(title, "n_{f} = %2i", ndf);
     copied = Func->DrawCopy("same");
     legend->AddEntry(copied, title);
     }
   }
 legend->Draw();
}