/// \file
/// \ingroup tutorial_fit
/// \notebook
/// Fitting a 2-D histogram (a variant)
/// This tutorial illustrates :
///  - how to create a 2-d function
///  - fill a 2-d histogram randomly from this function
///  - fit the histogram
///  - display the fitted function on top of the histogram (lego-plot)
///    using a surface plot in a sub-range of the histogram.
///
/// This example can be executed via the interpreter or/and the compiler
///
/// ~~~{.cpp}
///   root > .x fit2a.C
///   root > .x fit2a.C++
/// ~~~
///
/// \macro_image
/// \macro_output
/// \macro_code
///
/// \author Rene Brun

#include "TF2.h"
#include "TH2.h"
#include "TCutG.h"
#include "TMath.h"
#include "TCanvas.h"
#include "TStyle.h"

Double_t g2(Double_t *x, Double_t *par) {
   Double_t r1 = Double_t((x[0]-par[1])/par[2]);
   Double_t r2 = Double_t((x[1]-par[3])/par[4]);
   return par[0]*TMath::Exp(-0.5*(r1*r1+r2*r2));
}
Double_t fun2(Double_t *x, Double_t *par) {
   Double_t *p1 = &par[0];
   Double_t *p2 = &par[5];
   Double_t *p3 = &par[10];
   Double_t result = g2(x,p1) + g2(x,p2) + g2(x,p3);
   return result;
}

TCanvas *fit2a() {
   TCanvas *c = new TCanvas();
   gStyle->SetOptStat(kTRUE);
   gStyle->SetPalette(57);
   const Int_t npar = 15;
   Double_t f2params[npar] = {100,-3,3,-3,3,160,0,0.8,0,0.9,40,4,0.7,4,0.7};
   auto f2 = new TF2("f2",fun2,-10,10,-10,10, npar);
   f2->SetParameters(f2params);

   //Create an histogram and fill it randomly with f2
   auto h2 = new TH2F("h2","From f2",40,-10,10,40,-10,10);
   Int_t nentries = 100000;
   h2->FillRandom("f2",nentries);
   //Fit h2 with original function f2
   Float_t ratio = 4*nentries/100000;
   f2params[ 0] *= ratio;
   f2params[ 5] *= ratio;
   f2params[10] *= ratio;
   f2->SetParameters(f2params);
   h2->Fit("f2","N");
   auto cutg = new TCutG("cutg",5);
   cutg->SetPoint(0,-7,-7);
   cutg->SetPoint(1, 2,-7);
   cutg->SetPoint(2, 2, 2);
   cutg->SetPoint(3,-7, 2);
   cutg->SetPoint(4,-7,-7);
   h2->Draw("lego2 0");
   h2->SetFillColor(38);
   f2->SetNpx(80);
   f2->SetNpy(80);
   f2->Draw("surf1 same bb [cutg]");
   return c;
}