346 lines
9.3 KiB
C++
346 lines
9.3 KiB
C++
#ifndef AD_LIBARAY_H
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#define AD_LIBARAY_H
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#include "jSymbol.h"
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#include "Qk.h"
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#include <TROOT.h>
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#include <TSystem.h>
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#include <TAxis.h>
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#include <TF1.h>
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#include <TLatex.h>
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#include <TGraphErrors.h>
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#include <TApplication.h>
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#include <TCanvas.h>
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#define PI 3.14159265358979323846
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/// These are the coefficients for theritical distribution, index 1, 3 are not used.
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double Q[5] = {0};
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double B[5] = {0};
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double R1[5] = {0};
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double R2[5] = {0};
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double R3[5] = {0};
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///use for root fit
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double YE(double * x , double *par){
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/// x[0] = angle in radian;
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/// par[0] = a0;
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/// par[1] = a2;
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/// par[2] = a4;
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return par[0] + par[1] * LegendreP(2, x[0]) + par[2] * LegendreP(4, x[0]);
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}
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double Racah(int j1, int j2, int J, int j3, int j12, int j23){
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return pow(-1, j1+j2+j3+J) * SixJSymbol(j1, j2, j12, j3, J, j23);
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}
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double Rk(int k, int L1, int L2, int J1, int J2){
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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);
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}
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void PrintRk(int k){
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for( int J1 = 1; J1 < 8; J1 ++){
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printf("==============================\n");
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for( int J2 = 0; J2 < 8; J2++){
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int L = abs(J1 - J2);
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if( L == 0 ) L = 1;
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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));
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}
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}
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}
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double w(int M, double sigma){
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return 1./sqrt(2 * PI) / sigma * exp( - M*M / 2. / sigma/sigma);
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}
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//double wFix(int M, int J){
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// double sigma = 1;
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// switch (J) {
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// case 0 : sigma = 0.3989422804014327 ; break;
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// case 1 : sigma = 0.5723377817486753 ; break;
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// case 2 : sigma = 0.7013915463848625 ; break;
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// case 3 : sigma = 0.8091713162791643 ; break;
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// case 4 : sigma = 0.9037290722944527 ; break;
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// case 5 : sigma = 0.9890249035482789 ; break;
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// case 6 : sigma = 1.0673592868302038 ; break;
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// case 7 : sigma = 1.140210831444403 ; break;
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// case 8 : sigma = 1.208599155456379 ; break;
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// case 9 : sigma = 1.273313297516925 ; break;
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// case 10 : sigma = 1.335665551821612 ; break;
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// }
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//
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// return w(M, sigma);
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//}
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//
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//void Print_w_sum(){ /// Check the normalization of w(m), sum(w(m)) = 1 for all J.
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//
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// for( int J = 0; J < 11; J++){
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// double w_sum = 0;
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// for( int m = -J ; m < J+1; m++){
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// w_sum += w(m, J);
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// }
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// printf("%2d %.5f\n", J, w_sum);
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// }
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//}
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double Bk(int k, double J, double sigma){
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double norm_w = 0;
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for( int m = -J; m < J+1; m++) norm_w += w(m, sigma);
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double sum = 0;
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for(int m = -J; m < J+1 ; m++){
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sum += ( w(m, sigma) / norm_w ) * pow(-1, J-m) * pow(2*J+1,0.5) * CGcoeff(k, 0, J, m, J, -m);
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}
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return sum;
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}
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///use for fit a, delta
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double TheoryAD(double * x, double *par){
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/// par[0] = a;
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/// par[1] = delta;
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/// par[2] = sigma;
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/// par[3] = J;
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double result = 0;
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for( int k = 0; k <= 4; k += 2){
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result += Q[k]*Bk(k, par[3], par[2]) * LegendreP(k, x[0]) * ( R1[k] + 2*par[1]*R2[k] + par[1]*par[1]*R3[k] ) / (1 + par[1]*par[1] );
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}
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return result * par[0];
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}
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TGraphErrors * fitAD( std::vector<std::vector<double>> data_deg_count_error,
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double energy_keV,
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double detRadius_cm,
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double targetDistance_cm ,
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double detThickness_cm ,
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int Ji, int Jf,
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double sigma = 0){
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/// Calculate coefficient
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double * Qk = QK(energy_keV, detRadius_cm, targetDistance_cm, detThickness_cm);
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Q[0] = 1;
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Q[2] = Qk[0];
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Q[4] = Qk[1];
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delete Qk;
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int L = abs(Ji - Jf);
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if( L == 0 ) L = 1;
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for( int k = 0; k <= 4; k += 2){
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R1[k] = Rk(k, L , L , Ji, Jf);
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R2[k] = Rk(k, L , L+1, Ji, Jf);
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R3[k] = Rk(k, L+1, L+1, Ji, Jf);
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}
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for( int k = 0; k <=4; k += 2){
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printf("Qk(%d) : %10.8f, R1(%d) : %10.8f, R2(%d) : %10.8f, R3(%d) : %10.8f\n", k, Q[k], k, R1[k], k, R2[k], k, R3[k]);
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}
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/// Create TGraphEorrs
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const int dataSize = (int) data_deg_count_error.size();
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/// for TGraphErrors
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double x[dataSize];
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double y[dataSize];
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double ex[dataSize];
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double ey[dataSize];
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printf("============= Data :\n");
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for( int i = 0; i < dataSize; i++){
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printf("%2d | %8.2f, %8.2f(%4.0f) \n", i, data_deg_count_error[i][0], data_deg_count_error[i][1], data_deg_count_error[i][2]);
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x[i] = data_deg_count_error[i][0] * PI/180;
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y[i] = data_deg_count_error[i][1];
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ey[i] = data_deg_count_error[i][2];
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ex[i] = 0.;
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}
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printf("======================\n");
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TGraphErrors * gExp = new TGraphErrors( dataSize, x, y, ex, ey);
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gExp->SetTitle(Form("%.0f keV, detRadius = %.1f cm, detThickness = %.1f cm, distance = %.1f cm", energy_keV, detRadius_cm, detThickness_cm, targetDistance_cm));
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gExp->GetXaxis()->SetTitle("Angle [rad]");
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gExp->GetYaxis()->SetTitle("Data");
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TF1 * fit = new TF1("fit", TheoryAD, 0, PI, 4);
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fit->SetLineColor(2);
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fit->SetLineWidth(2);
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fit->SetNpx(1000);
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fit->SetParameter(0, 3000);
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fit->SetParameter(1, 1);
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fit->SetParameter(2, 1);
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fit->FixParameter(3, Ji);
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fit->SetParLimits(1, -30, 30);
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fit->SetParLimits(2, 0.2, Ji);
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if( sigma > 0 ) fit->FixParameter(2, sigma);
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fit->GetXaxis()->SetTitle("Angle [rad]");
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fit->GetYaxis()->SetTitle("Data");
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gExp->Fit("fit");
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const Double_t * paraE2 = fit->GetParErrors();
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const Double_t * paraA2 = fit->GetParameters();
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printf("===================== \n");
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printf("Best fit Amp = %f(%f)\n", paraA2[0], paraE2[0]);
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printf("Best fit delta = %f(%f) = %f(%f) deg\n", paraA2[1], paraE2[1], atan(paraA2[1]) * 180/PI, atan(paraE2[1])*180/PI);
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printf("Best fit sigma = %f(%f) \n", paraA2[3], paraE2[3]);
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TCanvas * canvas = new TCanvas("canvas", "Fitting Angular Distribution", 600, 400);
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canvas->cd(1);
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gExp->Draw("AP*");
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fit->Draw("same");
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TLatex text;
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text.SetNDC();
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text.SetTextFont(82);
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text.SetTextSize(0.04);
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text.DrawLatex(0.12, 0.85, Form(" #delta: %5.2f(%5.2f) = %5.1f(%5.1f) deg", paraA2[1], paraE2[1], atan(paraA2[1]) * 180/PI, atan(paraE2[1])*180/PI));
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text.DrawLatex(0.12, 0.80, Form(" Amp: %5.1f(%5.1f)", paraA2[0], paraE2[0]));
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text.DrawLatex(0.12, 0.75, Form(" #sigma: %5.1f(%5.1f)", paraA2[2], paraE2[2]));
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text.SetTextColor(2);
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text.DrawLatex(0.8, 0.8, Form("%d->%d", Ji, Jf));
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for( int k = 0; k <= 4; k += 2) printf("Bk(%d) : %10.7f\n", k, Bk(k, Ji, paraA2[2]));
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return gExp;
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}
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void fitOldAD(std::vector<std::vector<double>> data_deg_count_error,
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double energy_keV,
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double detRadius_cm,
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double targetDistance_cm ,
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double detThickness_cm ,
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int Ji, int Jf,
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double sigma){
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/// Calculate coefficient
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double * Qk = QK(energy_keV, detRadius_cm, targetDistance_cm, detThickness_cm);
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Q[0] = 1;
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Q[2] = Qk[0];
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Q[4] = Qk[1];
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delete Qk;
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int L = abs(Ji - Jf);
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if( L == 0 ) L = 1;
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for( int k = 0; k <= 4; k += 2){
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B[k] = Bk(k, Ji, sigma);
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R1[k] = Rk(k, L , L , Ji, Jf);
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R2[k] = Rk(k, L , L+1, Ji, Jf);
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R3[k] = Rk(k, L+1, L+1, Ji, Jf);
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}
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for( int k = 0; k <=4; k += 2){
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printf("Qk(%d) : %f, Bk(%d) : %f, R1(%d) : %f, R2(%d) : %f, R3(%d) : %f\n", k, Q[k], k, B[k], k, R1[k], k, R2[k], k, R3[k]);
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}
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/// Create TGraphEorrs
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const int dataSize = (int) data_deg_count_error.size();
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/// for TGraphErrors
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double x[dataSize];
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double y[dataSize];
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double ex[dataSize];
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double ey[dataSize];
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printf("============= Data :\n");
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for( int i = 0; i < dataSize; i++){
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printf("%2d | %8.2f, %8.2f(%4.0f) \n", i, data_deg_count_error[i][0], data_deg_count_error[i][1], data_deg_count_error[i][2]);
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x[i] = data_deg_count_error[i][0] * PI/180;
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y[i] = data_deg_count_error[i][1];
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ey[i] = data_deg_count_error[i][2];
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ex[i] = 0.;
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}
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printf("======================\n");
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TGraphErrors * gExp = new TGraphErrors( dataSize, x, y, ex, ey);
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gExp->SetTitle("");
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gExp->GetXaxis()->SetTitle("Angle [rad]");
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gExp->GetYaxis()->SetTitle("Data");
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///======== Fitting the experimental distribution with a0+ a2*P(2,cos(theta)) + a4 * P(4, cos(theta))
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TF1 * f1 = new TF1("f1", YE, 0, PI, 3);
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f1->SetLineColor(4);
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f1->SetLineWidth(2);
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f1->SetNpx(1000);
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f1->SetParameter(0, 2000);
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f1->SetParameter(1, -2000);
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f1->SetParameter(2, 2000);
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gExp->Fit("f1", "");
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const Double_t* paraE = f1->GetParErrors();
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const Double_t* paraA = f1->GetParameters();
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double A0 = paraA[0];
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///=================================== Find Chi-sq
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std::vector<double> deltaDeg;
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std::vector<double> LogChiSq;
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for( float deltaAngle = -90; deltaAngle <= 90 ; deltaAngle += 2. ){
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double delta = tan(deltaAngle * PI/ 180.);
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double chiSq = 0;
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for( int i = 0; i < dataSize; i++){
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double YT = 0;
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for( int k = 0; k <= 4; k += 2){
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YT += Q[k] * B[k] * LegendreP(k, x[i] * PI/180.) * ( R1[k] + 2 * delta * R2[k] + delta*delta* R3[k] ) / (1 + delta * delta) ;
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}
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chiSq += pow( A0 * YT - y[i], 2)/ dataSize / ey[i] / ey[i];
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}
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deltaDeg.push_back(deltaAngle);
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LogChiSq.push_back(log(chiSq));
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//printf(" %6.2f deg, %8.3f \n", deltaAngle, log(chiSq));
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}
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TGraph * gDelta = new TGraph((int) deltaDeg.size(), &deltaDeg[0], &LogChiSq[0]);
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gDelta->SetTitle("");
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gDelta->GetXaxis()->SetTitle("aTan(Mixing Ratio) [Deg]");
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gDelta->GetYaxis()->SetTitle("Log(chi-sq)");
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///======== Plot
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TCanvas * c1 = new TCanvas("c1", "Chi-sq of mixing ratio", 1000, 500);
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c1->Divide(2, 1);
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c1->cd(1);
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gExp->Draw("AP*");
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c1->cd(2);
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gDelta->Draw("APL*");
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}
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#endif
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