/**************************************************************************
 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
 *                                                                        *
 * Author: The ALICE Off-line Project.                                    *
 * Contributors are mentioned in the code where appropriate.              *
 *                                                                        *
 * Permission to use, copy, modify and distribute this software and its   *
 * documentation strictly for non-commercial purposes is hereby granted   *
 * without fee, provided that the above copyright notice appears in all   *
 * copies and that both the copyright notice and this permission notice   *
 * appear in the supporting documentation. The authors make no claims     *
 * about the suitability of this software for any purpose. It is          *
 * provided "as is" without express or implied warranty.                  *
 **************************************************************************/

/* $Id$ */

//-------------------------------------------------------------------------
//        Class AliMUONFastTracking 
//
//  Manager for the fast simulation of tracking in the muon spectrometer
//  This class reads the lookup tables containing the parameterization 
//  of the deltap, deltatheta, deltaphi for different background levels
//  and provides the related smeared parameters. 
//  Used by AliFastMuonTrackingEff, AliFastMuonTrackingAcc, 
//  AliFastMuonTrackingRes. 
//-------------------------------------------------------------------------

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#include <Riostream.h>
#include <TF1.h>
#include <TFile.h>
#include <TH3.h>
#include <TMath.h>
#include <TRandom.h>
#include <TSpline.h>

#include "AliMUONFastTracking.h"
#include "AliMUONFastTrackingEntry.h"

using std::cout;
using std::endl;
ClassImp(AliMUONFastTracking)


AliMUONFastTracking* AliMUONFastTracking::fgMUONFastTracking=NULL;

static Double_t FitP(Double_t *x, Double_t *par){
// Fit function
    Double_t dx = x[0] - par[0];
    Double_t dx2 = x[0] - par[4];
    Double_t sigma = par[1] * ( 1 + par[2] * dx);
    if (sigma == 0) {    

	return 0.;
    }
    Double_t fasymm = TMath::Exp(-0.5 * dx * dx / (sigma * sigma));
    Double_t sigma2 = par[1] * par[5];
    Double_t fgauss = TMath::Exp(-0.5 * dx2 * dx2 / (sigma2 * sigma2));
    Double_t value = fasymm + par[3] * fgauss; 
    return TMath::Abs(value);
} 

AliMUONFastTracking::AliMUONFastTracking(const AliMUONFastTracking & ft):
    TObject(),
    fNbinp(10),
    fPmin(0.),
    fPmax(200.),
    fDeltaP((fPmax-fPmin)/fNbinp),
    fNbintheta(10),
    fThetamin(2.),
    fThetamax(9.),
    fDeltaTheta((fThetamax-fThetamin)/fNbintheta),
    fNbinphi(10),
    fPhimin(-180.),
    fPhimax(180.),
    fDeltaPhi((fPhimax-fPhimin)/fNbinphi),
    fPrintLevel(1),
    fBkg(0.),
    fSpline(0),
    fClusterFinder(kOld)									 
{
// Copy constructor
    ft.Copy(*this);
}


AliMUONFastTracking* AliMUONFastTracking::Instance()
{ 
// Set random number generator 
    if (fgMUONFastTracking) {
	return fgMUONFastTracking;
    } else {
	fgMUONFastTracking = new AliMUONFastTracking();
	return fgMUONFastTracking;
    }
}

AliMUONFastTracking::AliMUONFastTracking():
    fNbinp(10),
    fPmin(0.),
    fPmax(200.),
    fDeltaP((fPmax-fPmin)/fNbinp),
    fNbintheta(10),
    fThetamin(2.),
    fThetamax(9.),
    fDeltaTheta((fThetamax-fThetamin)/fNbintheta),
    fNbinphi(10),
    fPhimin(-180.),
    fPhimax(180.),
    fDeltaPhi((fPhimax-fPhimin)/fNbinphi),
    fPrintLevel(1),
    fBkg(0.),
    fSpline(0),
    fClusterFinder(kOld)
{
//
// constructor
//
  for (Int_t i = 0; i<20;i++) {
    for (Int_t j = 0; j<20; j++) {
      for (Int_t k = 0; k<20; k++) {
	fFitp[i][j][k] = 0x0;
      }
    }
  }
}

void AliMUONFastTracking::Init(Float_t bkg)
{
  //
  //  Initialization
  //
  for (Int_t ip=0; ip< fNbinp; ip++){
    for (Int_t itheta=0; itheta< fNbintheta; itheta++){
      for (Int_t iphi=0; iphi< fNbinphi; iphi++){
	fCurrentEntry[ip][itheta][iphi] = new AliMUONFastTrackingEntry;
	for (Int_t ibkg=0; ibkg<4; ibkg++){
	  fEntry[ip][itheta][iphi][ibkg] = new AliMUONFastTrackingEntry;
	}
      }
    }
  }
  
  char filename [100]; 
  if (fClusterFinder==kOld) snprintf (filename, 100, "$(ALICE_ROOT)/FASTSIM/data/MUONtrackLUT.root"); 
  else snprintf (filename, 100, "$(ALICE_ROOT)/FASTSIM/data/MUONtrackLUT-AZ.root"); 

  TFile *file = new TFile(filename); 
  ReadLUT(file);
  SetBackground(bkg);
  UseSpline(0);
}


void AliMUONFastTracking::ReadLUT(TFile* file)
{
  //
  // read the lookup tables from file
  //
  TH3F *heff[5][3], *hacc[5][3], *hmeanp, *hsigmap, *hsigma1p, *hchi2p;
  TH3F *hnormg2, *hmeang2, *hsigmag2, *hmeantheta, *hsigmatheta, *hchi2theta;
  TH3F *hmeanphi, *hsigmaphi, *hchi2phi;
  char tag[40], tag2[40]; 
  
  printf ("Reading parameters from LUT file %s...\n",file->GetName());

  const Float_t kBkg[4] = {0, 0.5, 1, 2};
  for (Int_t ibkg=0; ibkg<4; ibkg++) {
    snprintf (tag, 40, "BKG%g",kBkg[ibkg]); 
    file->cd(tag);
    for (Int_t isplp = 0; isplp<kSplitP; isplp++) { 
      for (Int_t ispltheta = 0; ispltheta<kSplitTheta; ispltheta++) { 
	snprintf (tag2, 40, "heff[%d][%d]",isplp,ispltheta); 
	heff[isplp][ispltheta] = (TH3F*)gDirectory->Get(tag2);
	snprintf (tag2, 40, "hacc[%d][%d]",isplp,ispltheta); 
	hacc[isplp][ispltheta] = (TH3F*)gDirectory->Get(tag2);
      }
    }    
    hmeanp      = (TH3F*)gDirectory->Get("hmeanp");
    hsigmap     = (TH3F*)gDirectory->Get("hsigmap");
    hsigma1p    = (TH3F*)gDirectory->Get("hsigma1p");
    hchi2p      = (TH3F*)gDirectory->Get("hchi2p");
    hnormg2     = (TH3F*)gDirectory->Get("hnormg2");
    hmeang2     = (TH3F*)gDirectory->Get("hmeang2");
    hsigmag2    = (TH3F*)gDirectory->Get("hsigmag2");
    hmeantheta  = (TH3F*)gDirectory->Get("hmeantheta");
    hsigmatheta = (TH3F*)gDirectory->Get("hsigmatheta");
    hchi2theta  = (TH3F*)gDirectory->Get("hchi2theta");
    hmeanphi    = (TH3F*)gDirectory->Get("hmeanphi");
    hsigmaphi   = (TH3F*)gDirectory->Get("hsigmaphi");
    hchi2phi    = (TH3F*)gDirectory->Get("hchi2phi");
    
    for (Int_t ip=0; ip<fNbinp ;ip++) {
      for (Int_t itheta=0; itheta<fNbintheta ;itheta++) {
	for (Int_t iphi=0; iphi<fNbinphi ;iphi++) {
	  Float_t p     = fPmin     + fDeltaP     * (ip     + 0.5);
	  Float_t theta = fThetamin + fDeltaTheta * (itheta + 0.5);
	  Float_t phi   = fPhimin   + fDeltaPhi   * (iphi   + 0.5);
	  
	  fEntry[ip][itheta][iphi][ibkg]->SetP(p);
	  fEntry[ip][itheta][iphi][ibkg]->SetMeanp(hmeanp->GetBinContent(ip+1,itheta+1,iphi+1));
	  fEntry[ip][itheta][iphi][ibkg]->SetSigmap(TMath::Abs(hsigmap->GetBinContent(ip+1,itheta+1,iphi+1)));
	  fEntry[ip][itheta][iphi][ibkg]->SetSigma1p(hsigma1p->GetBinContent(ip+1,itheta+1,iphi+1));
	  fEntry[ip][itheta][iphi][ibkg]->SetChi2p(hchi2p->GetBinContent(ip+1,itheta+1,iphi+1));
	  fEntry[ip][itheta][iphi][ibkg]->SetNormG2(hnormg2->GetBinContent(ip+1,itheta+1,iphi+1));
	  fEntry[ip][itheta][iphi][ibkg]->SetMeanG2(hmeang2->GetBinContent(ip+1,itheta+1,iphi+1));
	  if (ibkg == 0)  fEntry[ip][itheta][iphi][ibkg]->SetSigmaG2(9999);
	  else fEntry[ip][itheta][iphi][ibkg]->SetSigmaG2(hsigmag2->GetBinContent(ip+1,itheta+1,iphi+1));
	  fEntry[ip][itheta][iphi][ibkg]->SetTheta(theta);
	  fEntry[ip][itheta][iphi][ibkg]->SetMeantheta(hmeantheta->GetBinContent(ip+1,itheta+1,iphi+1));
	  fEntry[ip][itheta][iphi][ibkg]->SetSigmatheta(TMath::Abs(hsigmatheta->GetBinContent(ip+1,itheta+1,iphi+1)));
	  fEntry[ip][itheta][iphi][ibkg]->SetChi2theta(hchi2theta->GetBinContent(ip+1,itheta+1,iphi+1));
	  fEntry[ip][itheta][iphi][ibkg]->SetPhi(phi);
	  fEntry[ip][itheta][iphi][ibkg]->SetMeanphi(hmeanphi->GetBinContent(ip+1,itheta+1,iphi+1));
	  fEntry[ip][itheta][iphi][ibkg]->SetSigmaphi(TMath::Abs(hsigmaphi->GetBinContent(ip+1,itheta+1,iphi+1)));
	  fEntry[ip][itheta][iphi][ibkg]->SetChi2phi(hchi2phi->GetBinContent(ip+1,itheta+1,iphi+1));
	  for (Int_t i=0; i<kSplitP; i++) { 
	    for (Int_t j=0; j<kSplitTheta; j++) { 
	      fEntry[ip][itheta][iphi][ibkg]->SetAcc(i,j,hacc[i][j]->GetBinContent(ip+1,itheta+1,iphi+1));
	      fEntry[ip][itheta][iphi][ibkg]->SetEff(i,j,heff[i][j]->GetBinContent(ip+1,itheta+1,iphi+1));
	    }
	  }
	} // iphi 
      }  // itheta
    }   // ip
  }    // ibkg

  TGraph *graph = new TGraph(3); 
  TF1 *f = new TF1("f","[0]+[1]*x"); 
  
  for (Int_t ip=0; ip< fNbinp; ip++){
    for (Int_t itheta=0; itheta< fNbintheta; itheta++){
      for (Int_t iphi=0; iphi< fNbinphi; iphi++){
	graph->SetPoint(0,0.5,fEntry[ip][itheta][iphi][1]->GetSigmaG2());
	graph->SetPoint(1,1,fEntry[ip][itheta][iphi][2]->GetSigmaG2());
	graph->SetPoint(2,2,fEntry[ip][itheta][iphi][3]->GetSigmaG2());
	graph->Fit("f","q"); 
	fEntry[ip][itheta][iphi][0]->SetSigmaG2(f->Eval(0)); 
      }
    }
  }
  f->Delete();
  graph->Delete();
  printf ("parameters read. \n");
}

void AliMUONFastTracking::GetBinning(Int_t &nbinp, Float_t &pmin, Float_t &pmax,
				     Int_t &nbintheta, Float_t &thetamin, 
				     Float_t &thetamax,
				     Int_t &nbinphi, Float_t &phimin, Float_t &phimax) const 
{
  //
  // gets the binning for the discrete parametrizations in the lookup table
  //
    nbinp = fNbinp;
    pmin  = fPmin;
    pmax  = fPmax;
    nbintheta = fNbintheta;
    thetamin  = fThetamin;
    thetamax  = fThetamax;
    nbinphi = fNbinphi;
    phimin  = fPhimin;
    phimax  = fPhimax;
}


void AliMUONFastTracking::GetIpIthetaIphi(Float_t p, Float_t theta, Float_t phi, 
					  Int_t charge, Int_t &ip, Int_t &itheta, 
					  Int_t &iphi) const
{
  //
  // gets the id of the cells in the LUT for a given (p,theta,phi, charge)
  //
    if (charge < 0) phi = -phi;
    ip           = Int_t (( p - fPmin ) / fDeltaP);
    itheta       = Int_t (( theta - fThetamin ) / fDeltaTheta);
    iphi         = Int_t (( phi - fPhimin ) / fDeltaPhi);
    
    
    if (ip< 0) 	ip = 0;
    if (ip>= fNbinp) ip = fNbinp-1;
    if (itheta< 0) itheta = 0;
    if (itheta>= fNbintheta) itheta = fNbintheta-1;
    
    if (iphi< 0) iphi = 0;
    if (iphi>= fNbinphi) iphi = fNbinphi-1;
}

void AliMUONFastTracking::GetSplit(Int_t ip, Int_t itheta, 
				   Int_t &nSplitP, Int_t &nSplitTheta) const 
{ 
  //
  // the first cell is splitted in more bins for theta and momentum
  // parameterizations. Get the number of divisions for the splitted bins
  //
  if (ip==0) nSplitP = 5; 
  else nSplitP = 2; 
  if (itheta==0) nSplitTheta = 3; 
  else nSplitTheta = 1; 
}

Float_t AliMUONFastTracking::Efficiency(Float_t p,   Float_t theta, 
					Float_t phi, Int_t charge){
  //
  // gets the tracking efficiency
  //
  Int_t ip=0, itheta=0, iphi=0;
  GetIpIthetaIphi(p,theta,phi,charge,ip,itheta,iphi);
  Int_t nSplitP, nSplitTheta; 
  GetSplit(ip,itheta,nSplitP,nSplitTheta); 

  Float_t dp = p - fPmin;
  Int_t ibinp  = Int_t(nSplitP*(dp - fDeltaP * Int_t(dp / fDeltaP))/fDeltaP); 
  Float_t dtheta = theta - fThetamin;
  Int_t ibintheta  = Int_t(nSplitTheta*(dtheta - fDeltaTheta * Int_t(dtheta / fDeltaTheta))/fDeltaTheta); 
  Float_t eff = fCurrentEntry[ip][itheta][iphi]->GetEff(ibinp,ibintheta);
  return eff;   
}

Float_t AliMUONFastTracking::Acceptance(Float_t p,   Float_t theta, 
					Float_t phi, Int_t charge){
  //
  // gets the geometrical acceptance
  //
  if (theta<fThetamin || theta>fThetamax) return 0; 
  
  Int_t ip=0, itheta=0, iphi=0;
  GetIpIthetaIphi(p,theta,phi,charge,ip,itheta,iphi);
  Int_t nSplitP, nSplitTheta; 
  GetSplit(ip,itheta,nSplitP,nSplitTheta); 
  // central value and corrections with spline 
  
  Float_t dp = p - fPmin;
  Int_t ibinp  = Int_t(nSplitP*(dp - fDeltaP * Int_t(dp / fDeltaP))/fDeltaP); 
  Float_t dtheta = theta - fThetamin;
  Int_t ibintheta  = Int_t(nSplitTheta*(dtheta - fDeltaTheta * Int_t(dtheta / fDeltaTheta))/fDeltaTheta); 
  Float_t acc = fCurrentEntry[ip][itheta][iphi]->GetAcc(ibinp,ibintheta);
  return acc;   
}

Float_t AliMUONFastTracking::MeanP(Float_t p,   Float_t theta, 
			    Float_t phi, Int_t charge) const
{
  //
  // gets the mean value of the prec-pgen distribution
  //
    Int_t ip=0, itheta=0, iphi=0;
    GetIpIthetaIphi(p,theta,phi,charge,ip,itheta,iphi);
    return fCurrentEntry[ip][itheta][iphi]->GetMeanp();
}

Float_t AliMUONFastTracking::SigmaP(Float_t p,   Float_t theta, 
				    Float_t phi, Int_t charge) const
{
  //
  // gets the width of the prec-pgen distribution
  //
    Int_t ip=0, itheta=0, iphi=0;
    Int_t index;
    GetIpIthetaIphi(p,theta,phi,charge,ip,itheta,iphi);
    // central value and corrections with spline 
    Float_t sigmap = fCurrentEntry[ip][itheta][iphi]->GetSigmap();
    if (!fSpline) return sigmap;
    // corrections vs p, theta, phi 
    index = iphi + fNbinphi * itheta;
    Double_t xmin,ymin,xmax,ymax;
    Float_t frac1 = fSplineSigmap[index][0]->Eval(p)/sigmap; 
    
    if (p>fPmax-fDeltaP/2.) {
	Float_t s1 = fCurrentEntry[fNbinp-1][itheta][iphi]->GetSigmap();
	Float_t s2 = fCurrentEntry[fNbinp-2][itheta][iphi]->GetSigmap();
	Float_t s3 = fCurrentEntry[fNbinp-3][itheta][iphi]->GetSigmap();
	Float_t p1  = fDeltaP * (fNbinp - 1 + 0.5) + fPmin;
	Float_t p2  = fDeltaP * (fNbinp - 2 + 0.5) + fPmin;
	Float_t p3  = fDeltaP * (fNbinp - 3 + 0.5) + fPmin;
	Float_t p12 = p1 * p1, p22 = p2 * p2, p32 = p3 * p3;
	Float_t d = p12*p2 + p1*p32 + p22*p3 - p32*p2 - p3*p12 - p22*p1;
	Float_t a = (s1*p2 + p1*s3 + s2*p3 - s3*p2 - p3*s1 - s2*p1) / d;
	Float_t b = (p12*s2 + s1*p32 + p22*s3 - p32*s2 - s3*p12 - p22*s1)/d;
	Float_t c = (p12*p2*s3 + p1*p32*s2 + p22*p3*s1 
		     - p32*p2*s1 - p3*p12*s2 - p22*p1*s3) / d;
	Float_t sigma = a * p * p + b * p + c;
  	frac1 = sigma/sigmap;
    }
    index = iphi + fNbinphi * ip;
    fSplineEff[index][1]->GetKnot(0,xmin,ymin);
    fSplineEff[index][1]->GetKnot(9,xmax,ymax);
    if (theta>xmax) theta = xmax;
    Float_t frac2 = fSplineSigmap[index][1]->Eval(theta)/sigmap; 
    index = itheta + fNbintheta * ip;
    fSplineEff[index][2]->GetKnot(0,xmin,ymin);
    fSplineEff[index][2]->GetKnot(9,xmax,ymax);
    if (phi>xmax) phi = xmax;
    Float_t frac3 = fSplineSigmap[index][2]->Eval(phi)/sigmap;
    Float_t sigmatot = sigmap * frac1 * frac2 * frac3;
    if (sigmatot<0) sigmatot = sigmap;
    return sigmatot;
}

Float_t AliMUONFastTracking::Sigma1P(Float_t p,   Float_t theta, 
			    Float_t phi, Int_t charge) const
{
  //
  // gets the width correction of the prec-pgen distribution (see FitP)
  //
    Int_t ip=0, itheta=0, iphi=0;
    GetIpIthetaIphi(p,theta,phi,charge,ip,itheta,iphi);
    if (p>fPmax) {
	// linear extrapolation of sigmap for p out of range 
	Float_t s1 = fCurrentEntry[fNbinp-1][itheta][iphi]->GetSigma1p();
	Float_t s2 = fCurrentEntry[fNbinp-2][itheta][iphi]->GetSigma1p();
	Float_t p1  = fDeltaP * (fNbinp - 1 + 0.5) + fPmin;
	Float_t p2  = fDeltaP * (fNbinp - 2 + 0.5) + fPmin;
	Float_t sigma = 1./(p1-p2) * ( (s1-s2)*p + (s2-s1)*p1 + s1*(p1-p2) ); 
	return sigma;
    }
    else return fCurrentEntry[ip][itheta][iphi]->GetSigma1p();
}

Float_t AliMUONFastTracking::NormG2(Float_t p,   Float_t theta, 
				    Float_t phi, Int_t charge) const
{
  //
  // gets the relative normalization of the background
  // (gaussian) component in the prec-pgen distribution
  //
    Int_t ip=0, itheta=0, iphi=0;
    GetIpIthetaIphi(p,theta,phi,charge,ip,itheta,iphi);
    if (p>fPmax) {
	// linear extrapolation of sigmap for p out of range 
	Float_t s1 = fCurrentEntry[fNbinp-1][itheta][iphi]->GetNormG2();
	Float_t s2 = fCurrentEntry[fNbinp-2][itheta][iphi]->GetNormG2();
	Float_t p1  = fDeltaP * (fNbinp - 1 + 0.5) + fPmin;
	Float_t p2  = fDeltaP * (fNbinp - 2 + 0.5) + fPmin;
	Float_t norm = 1./(p1-p2) * ( (s1-s2)*p + (s2-s1)*p1 + s1*(p1-p2) ); 
	return norm;
    }
    else return fCurrentEntry[ip][itheta][iphi]->GetNormG2();
}

Float_t AliMUONFastTracking::MeanG2(Float_t p,   Float_t theta, 
				    Float_t phi, Int_t charge) const
{
  //
  // gets the mean value of the background
  // (gaussian) component in the prec-pgen distribution
  //
    Int_t ip=0, itheta=0, iphi=0;
    GetIpIthetaIphi(p,theta,phi,charge,ip,itheta,iphi);
    if (p>fPmax) {
	// linear extrapolation of sigmap for p out of range 
	Float_t s1 = fCurrentEntry[fNbinp-1][itheta][iphi]->GetMeanG2();
	Float_t s2 = fCurrentEntry[fNbinp-2][itheta][iphi]->GetMeanG2();
	Float_t p1  = fDeltaP * (fNbinp - 1 + 0.5) + fPmin;
	Float_t p2  = fDeltaP * (fNbinp - 2 + 0.5) + fPmin;
	Float_t norm = 1./(p1-p2) * ( (s1-s2)*p + (s2-s1)*p1 + s1*(p1-p2) ); 
	return norm;
    }
    else return fCurrentEntry[ip][itheta][iphi]->GetMeanG2();
}

Float_t AliMUONFastTracking::SigmaG2(Float_t p,   Float_t theta, 
				     Float_t phi, Int_t charge) const
{
  //
  // gets the width of the background
  // (gaussian) component in the prec-pgen distribution
  //
    Int_t ip=0, itheta=0, iphi=0;
    GetIpIthetaIphi(p,theta,phi,charge,ip,itheta,iphi);
    if (p>fPmax) {
	// linear extrapolation of sigmap for p out of range 
	Float_t s1 = fCurrentEntry[fNbinp-1][itheta][iphi]->GetSigmaG2();
	Float_t s2 = fCurrentEntry[fNbinp-2][itheta][iphi]->GetSigmaG2();
	Float_t p1  = fDeltaP * (fNbinp - 1 + 0.5) + fPmin;
	Float_t p2  = fDeltaP * (fNbinp - 2 + 0.5) + fPmin;
	Float_t sigma = 1./(p1-p2) * ( (s1-s2)*p + (s2-s1)*p1 + s1*(p1-p2) ); 
	return sigma;
    }
    else return fCurrentEntry[ip][itheta][iphi]->GetSigmaG2();
}


Float_t AliMUONFastTracking::MeanTheta(Float_t p,   Float_t theta, 
				       Float_t phi, Int_t charge) const
{
  //
  // gets the mean value of the thetarec-thetagen distribution
  //
    Int_t ip=0, itheta=0, iphi=0;
    GetIpIthetaIphi(p,theta,phi,charge,ip,itheta,iphi);
    return fCurrentEntry[ip][itheta][iphi]->GetMeantheta();
}

Float_t AliMUONFastTracking::SigmaTheta(Float_t p,   Float_t theta,  
			    Float_t phi, Int_t charge) const
{
  //
  // gets the width of the thetarec-thetagen distribution
  //
  Int_t ip=0, itheta=0, iphi=0;
  Int_t index;
  GetIpIthetaIphi(p,theta,phi,charge,ip,itheta,iphi);
  // central value and corrections with spline 
  Float_t sigmatheta = fCurrentEntry[ip][itheta][iphi]->GetSigmatheta();
  if (!fSpline) return sigmatheta;
  // corrections vs p, theta, phi 
  index = iphi + fNbinphi * itheta;
  Double_t xmin,ymin,xmax,ymax;
  Float_t frac1 = fSplineSigmatheta[index][0]->Eval(p)/sigmatheta; 
  if (p>fPmax-fDeltaP/2.) {
    // linear extrapolation of sigmap for p out of range 
    Float_t s1 = fCurrentEntry[fNbinp-1][itheta][iphi]->GetSigmatheta();
    Float_t s2 = fCurrentEntry[fNbinp-2][itheta][iphi]->GetSigmatheta();
    Float_t p1  = fDeltaP * (fNbinp - 1 + 0.5) + fPmin;
    Float_t p2  = fDeltaP * (fNbinp - 2 + 0.5) + fPmin;
    Float_t sigma = 1./(p1-p2) * ( (s1-s2)*p + (s2-s1)*p1 + s1*(p1-p2) ); 
    frac1=sigma/sigmatheta;
  }
  index = iphi + fNbinphi * ip;
  fSplineEff[index][1]->GetKnot(0,xmin,ymin);
  fSplineEff[index][1]->GetKnot(9,xmax,ymax);
  if (theta>xmax) theta = xmax;
  Float_t frac2 = fSplineSigmatheta[index][1]->Eval(theta)/sigmatheta; 
  index = itheta + fNbintheta * ip;
  fSplineEff[index][2]->GetKnot(0,xmin,ymin);
  fSplineEff[index][2]->GetKnot(9,xmax,ymax);
  if (phi>xmax) phi = xmax;
  Float_t frac3 = fSplineSigmatheta[index][2]->Eval(phi)/sigmatheta;
  return sigmatheta * frac1 * frac2 * frac3;
}


Float_t AliMUONFastTracking::MeanPhi(Float_t p,   Float_t theta, 
			    Float_t phi, Int_t charge) const
{
  //
  // gets the mean value of the phirec-phigen distribution
  //
  Int_t ip=0, itheta=0, iphi=0;
  GetIpIthetaIphi(p,theta,phi,charge,ip,itheta,iphi);
  return fCurrentEntry[ip][itheta][iphi]->GetMeanphi();
}

Float_t AliMUONFastTracking::SigmaPhi(Float_t p,   Float_t theta, 
			    Float_t phi, Int_t charge){
  //
  // gets the width of the phirec-phigen distribution
  //
  Int_t ip=0, itheta=0, iphi=0;
  Int_t index;
  GetIpIthetaIphi(p,theta,phi,charge,ip,itheta,iphi);
  // central value and corrections with spline 
  Float_t sigmaphi = fCurrentEntry[ip][itheta][iphi]->GetSigmaphi();
  if (!fSpline) return sigmaphi;
  // corrections vs p, theta, phi 
  index = iphi + fNbinphi * itheta;
  Float_t frac1 = fSplineSigmaphi[index][0]->Eval(p)/sigmaphi; 
  Double_t xmin,ymin,xmax,ymax;
  if (p>fPmax-fDeltaP/2.) {
    Float_t s1 = fCurrentEntry[fNbinp-1][itheta][iphi]->GetSigmaphi();
    Float_t s2 = fCurrentEntry[fNbinp-2][itheta][iphi]->GetSigmaphi();
    Float_t p1  = fDeltaP * (fNbinp - 1 + 0.5) + fPmin;
    Float_t p2  = fDeltaP * (fNbinp - 2 + 0.5) + fPmin;
    Float_t sigma = 1./(p1-p2) * ( (s1-s2)*p + (s2-s1)*p1 + s1*(p1-p2) ); 
    frac1 = sigma/sigmaphi;
  }
  
  index = iphi + fNbinphi * ip;
  fSplineEff[index][1]->GetKnot(0,xmin,ymin);
  fSplineEff[index][1]->GetKnot(9,xmax,ymax);
  if (theta>xmax) theta = xmax;
  Float_t frac2 = fSplineSigmaphi[index][1]->Eval(theta)/sigmaphi; 
  index = itheta + fNbintheta * ip;
  fSplineEff[index][2]->GetKnot(0,xmin,ymin);
  fSplineEff[index][2]->GetKnot(9,xmax,ymax);
  if (phi>xmax) phi = xmax;
  Float_t frac3 = fSplineSigmaphi[index][2]->Eval(phi)/sigmaphi;
  return sigmaphi * frac1 * frac2 * frac3;
}

void AliMUONFastTracking::SetSpline(){
  //
  // sets the spline functions for a smooth behaviour of the parameters
  // when going from one cell to another
  //
  printf ("Setting spline functions...");
  char splname[40];
  Double_t x[20][3];
  Double_t x2[50][3];
  Int_t nbins[3] = {fNbinp, fNbintheta, fNbinphi};
  Double_t xspl[20],yeff[50],ysigmap[20],ysigma1p[20];
  Double_t yacc[50], ysigmatheta[20],ysigmaphi[20];
  Double_t xsp2[50];
  // let's calculate the x axis for p, theta, phi
  
  Int_t i, ispline, ivar;
  for (i=0; i< fNbinp; i++) x[i][0] = fPmin + fDeltaP * (i + 0.5);
  for (i=0; i< fNbintheta; i++) x[i][1] = fThetamin + fDeltaTheta * (i + 0.5);
  for (i=0; i< fNbinphi; i++) x[i][2] = fPhimin + fDeltaPhi * (i + 0.5);
  
  for (i=0; i< 5 * fNbinp; i++) x2[i][0] = fPmin + fDeltaP * (i + 0.5)/5.;
  for (i=0; i< 5 * fNbintheta; i++) x2[i][1] = fThetamin + fDeltaTheta * (i + 0.5)/5.;
  for (i=0; i< 5 * fNbinphi; i++) x2[i][2] = fPhimin + fDeltaPhi * (i + 0.5)/5.;
  
  // splines in p
  ivar = 0; 
  for (i=0; i<nbins[ivar]; i++) xspl[i] = x[i][ivar];
  for (i=0; i<5 * nbins[ivar]; i++) xsp2[i] = x2[i][ivar];
  ispline=0;
  for (Int_t itheta=0; itheta< fNbintheta; itheta++){
    for (Int_t iphi=0; iphi< fNbinphi; iphi++){
      for (Int_t ip=0; ip<fNbinp; ip++) {
	ysigmap[ip]     = fCurrentEntry[ip][itheta][iphi]->GetSigmap();
	ysigma1p[ip]    = fCurrentEntry[ip][itheta][iphi]->GetSigma1p();
	ysigmatheta[ip] = fCurrentEntry[ip][itheta][iphi]->GetSigmatheta();
	ysigmaphi[ip]   = fCurrentEntry[ip][itheta][iphi]->GetSigmaphi();
      }
      if (fPrintLevel>3) cout << " creating new spline " << splname << endl;
      snprintf (splname, 40, "fSplineEff[%d][%d]",ispline,ivar);
      fSplineEff[ispline][ivar] = new TSpline3(splname,xsp2,yeff,5 * nbins[ivar]);
      snprintf (splname, 40, "fSplineAcc[%d][%d]",ispline,ivar);
      fSplineAcc[ispline][ivar] = new TSpline3(splname,xsp2,yacc,5 * nbins[ivar]);
      snprintf (splname, 40, "fSplineSigmap[%d][%d]",ispline,ivar);
      fSplineSigmap[ispline][ivar] = new TSpline3(splname,xspl,ysigmap,nbins[ivar]);
      snprintf (splname, 40, "fSplineSigma1p[%d][%d]",ispline,ivar);
      fSplineSigma1p[ispline][ivar] = new TSpline3(splname,xspl,ysigma1p,nbins[ivar]);
      snprintf (splname, 40, "fSplineSigmatheta[%d][%d]",ispline,ivar);
      fSplineSigmatheta[ispline][ivar] = new TSpline3(splname,xspl,ysigmatheta,nbins[ivar]);
      snprintf (splname, 40, "fSplineSigmaphi[%d][%d]",ispline,ivar);
      fSplineSigmaphi[ispline][ivar] = new TSpline3(splname,xspl,ysigmaphi,nbins[ivar]);
      ispline++;
    }
  }

  ivar = 1; 
  for (i=0; i<nbins[ivar]; i++) xspl[i] = x[i][ivar];
  ispline=0;
  for (Int_t ip=0; ip<fNbinp; ip++) {
    for (Int_t iphi=0; iphi< fNbinphi; iphi++){
      for (Int_t itheta=0; itheta< fNbintheta; itheta++){
	// for efficiency and acceptance let's take the central value
	ysigmap[itheta]     = fCurrentEntry[ip][itheta][iphi]->GetSigmap();
	ysigma1p[itheta]    = fCurrentEntry[ip][itheta][iphi]->GetSigma1p();
	ysigmatheta[itheta] = fCurrentEntry[ip][itheta][iphi]->GetSigmatheta();
	ysigmaphi[itheta]   = fCurrentEntry[ip][itheta][iphi]->GetSigmaphi();
      }
      if (fPrintLevel>3) cout << " creating new spline " << splname << endl;
      snprintf (splname, 40, "fSplineEff[%d][%d]",ispline,ivar);
      fSplineEff[ispline][ivar] = new TSpline3(splname,xspl,yeff, nbins[ivar]);
      snprintf (splname, 40, "fSplineAcc[%d][%d]",ispline,ivar);
      fSplineAcc[ispline][ivar] = new TSpline3(splname,xspl,yacc, nbins[ivar]);
      snprintf (splname, 40, "fSplineSigmap[%d][%d]",ispline,ivar);
      fSplineSigmap[ispline][ivar] = new TSpline3(splname,xspl,ysigmap,nbins[ivar]);
      snprintf (splname, 40, "fSplineSigma1p[%d][%d]",ispline,ivar);
      fSplineSigma1p[ispline][ivar] = new TSpline3(splname,xspl,ysigma1p,nbins[ivar]);
      snprintf (splname, 40, "fSplineSigmatheta[%d][%d]",ispline,ivar);
      fSplineSigmatheta[ispline][ivar] = new TSpline3(splname,xspl,ysigmatheta,nbins[ivar]);
      snprintf (splname, 40, "fSplineSigmaphi[%d][%d]",ispline,ivar);
      fSplineSigmaphi[ispline][ivar] = new TSpline3(splname,xspl,ysigmaphi,nbins[ivar]);
      ispline++;
    }
  }

  ivar = 2; 
  for (i=0; i<nbins[ivar]; i++) xspl[i] = x[i][ivar];
  ispline=0;
  for (Int_t ip=0; ip<fNbinp; ip++) {
    for (Int_t itheta=0; itheta< fNbintheta; itheta++){
      for (Int_t iphi=0; iphi< fNbinphi; iphi++){
	// for efficiency and acceptance let's take the central value
	ysigmap[iphi]     = fCurrentEntry[ip][itheta][iphi]->GetSigmap();
	ysigma1p[iphi]    = fCurrentEntry[ip][itheta][iphi]->GetSigma1p();
	ysigmatheta[iphi] = fCurrentEntry[ip][itheta][iphi]->GetSigmatheta();
	ysigmaphi[iphi]   = fCurrentEntry[ip][itheta][iphi]->GetSigmaphi();
      }
      if (fPrintLevel>3) cout << " creating new spline " << splname << endl;
      snprintf (splname, 40, "fSplineEff[%d][%d]",ispline,ivar);
      fSplineEff[ispline][ivar] = new TSpline3(splname,xspl,yeff, nbins[ivar]);
      snprintf (splname, 40, "fSplineAcc[%d][%d]",ispline,ivar);
      fSplineAcc[ispline][ivar] = new TSpline3(splname,xspl,yacc, nbins[ivar]);
      snprintf (splname, 40, "fSplineSigmap[%d][%d]",ispline,ivar);
      fSplineSigmap[ispline][ivar] = new TSpline3(splname,xspl,ysigmap,nbins[ivar]);
      snprintf (splname, 40, "fSplineSigma1p[%d][%d]",ispline,ivar);
      fSplineSigma1p[ispline][ivar] = new TSpline3(splname,xspl,ysigma1p,nbins[ivar]);
      snprintf (splname, 40, "fSplineSigmatheta[%d][%d]",ispline,ivar);
      fSplineSigmatheta[ispline][ivar] = new TSpline3(splname,xspl,ysigmatheta,nbins[ivar]);
      snprintf (splname, 40, "fSplineSigmaphi[%d][%d]",ispline,ivar);
      fSplineSigmaphi[ispline][ivar] = new TSpline3(splname,xspl,ysigmaphi,nbins[ivar]);
      ispline++;
    }
  }
  printf ("...done\n");
}
  
void AliMUONFastTracking::SetBackground(Float_t bkg){
  //
  // linear interpolation of the parameters in the LUT between 2 values where
  // the background has been actually calculated
  //
  if (bkg>2) printf ("WARNING: unsafe extrapolation!\n");
  fBkg = bkg;

  Float_t bkgLevel[4] = {0, 0.5, 1, 2}; // bkg values for which LUT is calculated
  Int_t ibkg;
  for (ibkg=0; ibkg<4; ibkg++) if ( bkg < bkgLevel[ibkg]) break;
  if (ibkg == 4) ibkg--;
  if (ibkg == 0) ibkg++;
  
  Float_t x0 = bkgLevel[ibkg-1];
  Float_t x1 = bkgLevel[ibkg];
  Float_t x = (bkg - x0) / (x1 - x0); 
  
  Float_t y0, y1;

  for (Int_t ip=0; ip< fNbinp; ip++){
    for (Int_t itheta=0; itheta< fNbintheta; itheta++){
      for (Int_t iphi=0; iphi< fNbinphi; iphi++){
	fCurrentEntry[ip][itheta][iphi]->SetP(fEntry[ip][itheta][iphi][ibkg]->GetP());
	fCurrentEntry[ip][itheta][iphi]->SetTheta(fEntry[ip][itheta][iphi][ibkg]->GetTheta());
	fCurrentEntry[ip][itheta][iphi]->SetPhi(fEntry[ip][itheta][iphi][ibkg]->GetPhi());
	fCurrentEntry[ip][itheta][iphi]->SetChi2p(-1);
	fCurrentEntry[ip][itheta][iphi]->SetChi2theta(-1);
	fCurrentEntry[ip][itheta][iphi]->SetChi2phi(-1);

	y0 = fEntry[ip][itheta][iphi][ibkg-1]->GetMeanp();
	y1 =   fEntry[ip][itheta][iphi][ibkg]->GetMeanp();
	fCurrentEntry[ip][itheta][iphi]      ->SetMeanp((y1 - y0) * x + y0);
	y0 = fEntry[ip][itheta][iphi][ibkg-1]->GetMeantheta();
	y1 =   fEntry[ip][itheta][iphi][ibkg]->GetMeantheta();
	fCurrentEntry[ip][itheta][iphi]      ->SetMeantheta((y1 - y0) * x +y0);
	y0 = fEntry[ip][itheta][iphi][ibkg-1]->GetMeanphi();
	y1 =   fEntry[ip][itheta][iphi][ibkg]->GetMeanphi();
	fCurrentEntry[ip][itheta][iphi]      ->SetMeanphi((y1 - y0) * x + y0);
	y0 = fEntry[ip][itheta][iphi][ibkg-1]->GetSigmap();
	y1 =   fEntry[ip][itheta][iphi][ibkg]->GetSigmap();
	fCurrentEntry[ip][itheta][iphi]      ->SetSigmap((y1 - y0) * x + y0);
	y0 = fEntry[ip][itheta][iphi][ibkg-1]->GetSigmatheta();
	y1 =   fEntry[ip][itheta][iphi][ibkg]->GetSigmatheta();
	fCurrentEntry[ip][itheta][iphi]      ->SetSigmatheta((y1 - y0) * x+y0);
	y0 = fEntry[ip][itheta][iphi][ibkg-1]->GetSigmaphi();
	y1 =   fEntry[ip][itheta][iphi][ibkg]->GetSigmaphi();
	fCurrentEntry[ip][itheta][iphi]      ->SetSigmaphi((y1 - y0) * x + y0);
	y0 = fEntry[ip][itheta][iphi][ibkg-1]->GetSigma1p();
	y1 =   fEntry[ip][itheta][iphi][ibkg]->GetSigma1p();
	fCurrentEntry[ip][itheta][iphi]      ->SetSigma1p((y1 - y0) * x + y0);
	y0 = fEntry[ip][itheta][iphi][ibkg-1]->GetNormG2();
	y1 =   fEntry[ip][itheta][iphi][ibkg]->GetNormG2();
	fCurrentEntry[ip][itheta][iphi]      ->SetNormG2((y1 - y0) * x + y0);
	y0 = fEntry[ip][itheta][iphi][ibkg-1]->GetMeanG2();
	y1 =   fEntry[ip][itheta][iphi][ibkg]->GetMeanG2();
	fCurrentEntry[ip][itheta][iphi]      ->SetMeanG2((y1 - y0) * x + y0);
	
	y0 = fEntry[ip][itheta][iphi][ibkg-1]->GetSigmaG2();
	y1 =   fEntry[ip][itheta][iphi][ibkg]->GetSigmaG2();
	fCurrentEntry[ip][itheta][iphi]      ->SetSigmaG2((y1 - y0) * x + y0);
	for (Int_t i=0; i<kSplitP; i++) {
	  for (Int_t j=0; j<kSplitTheta; j++) {
	    fCurrentEntry[ip][itheta][iphi]->SetAcc(i,j,fEntry[ip][itheta][iphi][ibkg]->GetAcc(i,j));
	    y0 = fEntry[ip][itheta][iphi][ibkg-1]->GetEff(i,j);
	    y1 =   fEntry[ip][itheta][iphi][ibkg]->GetEff(i,j);
	    fCurrentEntry[ip][itheta][iphi]->SetEff(i,j, (y1 - y0) * x + y0);
	  }
	}
      }
    }
  }
  SetSpline();
}

TF1* AliMUONFastTracking::GetFitP(Int_t ip,Int_t itheta,Int_t iphi) { 
  // gets the correct prec-pgen distribution for a given LUT cell 
  if (!fFitp[ip][itheta][iphi]) {
    char name[256];
    snprintf(name, 256, "fit_%d_%d_%d", ip, itheta, iphi);
    fFitp[ip][itheta][iphi] = new TF1(name ,FitP,-20.,20.,6);
    fFitp[ip][itheta][iphi]->SetNpx(500);    
    fFitp[ip][itheta][iphi]->SetParameters(0.,0.,0.,0.,0.,0.);    
  }
  return fFitp[ip][itheta][iphi]; 
}

AliMUONFastTracking& AliMUONFastTracking::operator=(const  AliMUONFastTracking& rhs)
{
// Assignment operator
    rhs.Copy(*this);
    return *this;
}

void AliMUONFastTracking::Copy(TObject&) const
{
    //
    // Copy 
    //
    Fatal("Copy","Not implemented!\n");
}