ADPlusPlus/ad++.cpp

#include "jSymbol.h"
#include "Qk.h"

#include <TROOT.h>
#include <TSystem.h>
#include <TAxis.h>
#include <TF1.h>
#include <TLatex.h>
#include <TGraphErrors.h>
#include <TApplication.h>
#include <TCanvas.h>


#define PI 3.14159265358979323846

double Racah(int j1, int j2, int J, int j3, int j12, int j23);
double Rk(int k, int L1, int L2, int J1, int J2);
void PrintRk(int k);
double w(int M, int J);
void Print_w_sum();
double Bk(int k, int J);
double YE(double * x , double *par);/// for root Fit


/// This is for general fit a, delta
double Q[5] = {0};
double B[5] = {0};
double R1[5] = {0};
double R2[5] = {0};
double R3[5] = {0};
double Fit(double * x, double *par);

int main(int argc, char **argv){

  TApplication theApp("App",&argc,argv);

  //========================== User input
  double energy_keV = 832;
  double detRadius_cm = 2;
  double targetDistance_cm = 20;
  double detThickness_cm = 10;

  double data[][3] = { { 150.00, 2441.44, 122},
                       { 131.75, 2580.11, 129},
                       {  90.00, 4652.08, 232},
                       {  48.75, 3023.17, 151} };


  const int Ji = 5;
  const int Jf = 4;
  //======================================

  /// detector acceptance
  double * Qk = QK(energy_keV, detRadius_cm, targetDistance_cm, detThickness_cm); 
  Q[0] = 1;
  Q[2] = Qk[0];
  Q[4] = Qk[1];
  
  printf("Qk2 : %f \n", Q[2]);
  printf("Qk4 : %f \n", Q[4]);

  const int dataSize = sizeof(data)/sizeof(double)/3;

  /// for TGraphErrors
  double x[dataSize];
  double y[dataSize];
  double ex[dataSize];
  double ey[dataSize];

  printf("============= Data :\n");
  for( int i = 0; i < dataSize; i++){
    printf("%2d | %8.2f, %8.2f(%4.0f) \n", i, data[i][0], data[i][1], data[i][2]);

    x[i] = data[i][0] * PI/180;
    y[i] = data[i][1];
    ey[i] = data[i][2];
    ex[i] = 0.;
  }
  printf("======================\n");

  TGraphErrors * gExp = new TGraphErrors( dataSize, x, y, ex, ey);
  gExp->SetTitle("");
  gExp->GetXaxis()->SetTitle("Angle [rad]");
  gExp->GetYaxis()->SetTitle("Data");
  
  TCanvas * c1 = new TCanvas("c1", "c1", 1000, 500);
  c1->Divide(2, 1);
  c1->cd(1);
  gExp->Draw("AP*");

  c1->Modified();
  gSystem->ProcessEvents();


  ///======== Fitting the experimental distribution with a0+ a2*P(2,cos(theta)) + a4 * P(4, cos(theta))
  TF1 * f1 = new TF1("f1", YE, 0, PI, 3);

  f1->SetLineColor(4);
  f1->SetLineWidth(2);
  f1->SetNpx(1000);
  f1->SetParameter(0, 2000);
  f1->SetParameter(1, -2000);
  f1->SetParameter(2, 2000);

  gExp->Fit("f1", "");

  const Double_t* paraE = f1->GetParErrors();
  const Double_t* paraA = f1->GetParameters();

  double A0 = paraA[0];
  double A2 = paraA[1];
  double A4 = paraA[2];

  ///=================================== Fit with Theritical


  int L = abs(Ji - Jf);
  if( L == 0 ) L = 1;


  for( int k = 0; k <= 4; k += 2){
    B[k] = Bk(k, Ji);
    R1[k] = Rk(k, L  , L  , Ji, Jf);
    R2[k] = Rk(k, L  , L+1, Ji, Jf);
    R3[k] = Rk(k, L+1, L+1, Ji, Jf);
  }

  std::vector<double> deltaDeg;
  std::vector<double> LogChiSq;

  for( float deltaAngle = -90; deltaAngle <= 90 ; deltaAngle += 2. ){

    double delta = tan(deltaAngle * PI/ 180.);

    double chiSq = 0;
    for( int i = 0; i < dataSize; i++){

      double YT = 0;

      for( int k = 0; k <= 4; k += 2){
        YT += Q[k] * B[k] * LegendreP(k, x[i]) * ( R1[k] + 2 * delta * R2[k] + delta*delta* R3[k] ) / (1 + delta * delta) ;
      }
      
      //printf("      YT : %f , YE : %f \n", A0 * YT, y[i]);
      
      chiSq += pow( A0 * YT - y[i], 2)/ dataSize / ey[i] / ey[i];

    }

    deltaDeg.push_back(deltaAngle);
    LogChiSq.push_back(log(chiSq));
    //printf(" %6.2f deg, %8.3f \n", deltaAngle, log(chiSq));
  }

  c1->cd(2);
  TGraph * gDelta = new TGraph((int) deltaDeg.size(), &deltaDeg[0], &LogChiSq[0]);
  gDelta->SetTitle("");
  gDelta->GetXaxis()->SetTitle("aTan(Mixing Ratio) [Deg]");
  gDelta->GetYaxis()->SetTitle("Log(chi-sq)");

  gDelta->Draw("APL*");

  c1->Modified();
  gSystem->ProcessEvents();

  ///=============================== Fit a, delta at once

  TF1 * fit = new TF1("fit", Fit, 0, PI, 2);
  fit->SetLineColor(2);
  fit->SetLineWidth(2);
  fit->SetNpx(1000);
  fit->SetParameter(0, 3000);
  fit->SetParameter(1, 1);
  
  gExp->Fit("fit", "q");

  const Double_t * paraE2 = fit->GetParErrors();
  const Double_t * paraA2 = fit->GetParameters();

  printf("===================== \n");
  printf("Best fit Amp   = %f(%f)\n", paraA2[0], paraE2[0]);
  printf("Best fit delta = %f(%f) = %f(%f) deg\n", paraA2[1], paraE2[1],  atan(paraA2[1]) * 180/PI,  atan(paraE2[1])*180/PI);

  c1->cd(1);
  fit->Draw("same");
  f1->Draw("same");

  TLatex text;
  text.SetNDC();
  text.SetTextFont(82);
  text.SetTextSize(0.04);

  text.DrawLatex(0.12, 0.85, Form("#delta : %5.1f(%5.1f) deg", atan(paraA2[1]) * 180/PI,  atan(paraE2[1])*180/PI));
  text.DrawLatex(0.12, 0.80, Form("Amp: %5.1f(%5.1f)", paraA2[0], paraE2[0]));

  text.SetTextColor(2);

  text.DrawLatex(0.8, 0.8, Form("%d->%d", Ji, Jf));

  printf("===================== Crtl+C to end.\n");

  theApp.Run();

  return 0;

}

//#########################
///use for root fit
double YE(double * x , double *par){
  /// x[0] = angle in radian;
  /// par[0] = a0;
  /// par[1] = a2;
  /// par[2] = a4;

  return par[0] + par[1] * LegendreP(2, x[0]) + par[2] * LegendreP(4, x[0]);
}

///use for fit a, delta
double Fit(double * x, double *par){
  /// par[0] = a;
  /// par[1] = delta;

  double result = 0;
  for( int k = 0; k <= 4; k += 2){

    result += Q[k]*B[k] * LegendreP(k, x[0]) * ( R1[k] + 2*par[1]*R2[k] + par[1]*par[1]*R3[k] ) / (1 + par[1]*par[1] );
  }
  
  return result * par[0];
}


double Racah(int j1, int j2, int J, int j3, int j12, int j23){

  return pow(-1, j1+j2+j3+J) * SixJSymbol(j1, j2, j12, j3, J, j23); 

}

double Rk(int k, int L1, int L2, int J1, int J2){

  return pow(-1, 1+J1-J2+L2-L1-k) * pow((2*J1+1)*(2*L1+1)*(2*L2+1), 0.5) * CGcoeff(k, 0, L1, 1, L2, -1) * Racah(J1, J1, L1, L2, k, J2);

}

void PrintRk(int k){

  for( int J1 = 1; J1 < 8; J1 ++){
    printf("==============================\n");
    for( int J2 = 0; J2 < 8; J2++){

      int L = abs(J1 - J2);
      if( L == 0 ) L = 1;
      printf("%d %d | %10.6f, %10.6f, %10.6f \n", J1, J2, Rk(k, L, L, J1, J2), Rk(k, L, L+1, J1, J2), Rk(k, L+1, L+1, J1, J2));
      
    }
  }
}

double w(int M, int J){
  double sigma = 1;
  switch (J) {
    case  0 : sigma = 0.3989422804014327 ; break;
    case  1 : sigma = 0.5723377817486753 ; break;
    case  2 : sigma = 0.7013915463848625 ; break;
    case  3 : sigma = 0.8091713162791643 ; break;
    case  4 : sigma = 0.9037290722944527 ; break;
    case  5 : sigma = 0.9890249035482789 ; break;
    case  6 : sigma = 1.0673592868302038 ; break;
    case  7 : sigma = 1.140210831444403  ; break;
    case  8 : sigma = 1.208599155456379  ; break;
    case  9 : sigma = 1.273313297516925  ; break;
    case 10 : sigma = 1.335665551821612  ; break;
  }

  return 1./sqrt(2 * PI) / sigma * exp( - M*M / 2. / sigma/sigma);
  
}

void Print_w_sum(){ /// Check the normalization of w(m), sum(w(m)) = 1 for all J.

  for( int J = 0; J < 11; J++){
    double w_sum = 0;
    for( int m = -J ; m < J+1; m++){
      w_sum += w(m, J);
    }
    printf("%2d %.5f\n", J, w_sum);
  }
}

double Bk(int k, int J){

  double sum = 0;
  for(int m = -J; m < J+1 ; m++){
    sum += w(m, J) * pow(-1, J-m) * pow(2*J+1,0.5) * CGcoeff(k, 0, J, m, J, -m);
  }

  return sum;
  
}