From 1a8a165b80810e37beb42a598f328bb5b6f630fb Mon Sep 17 00:00:00 2001 From: "Ryan@iMac" Date: Tue, 11 Oct 2022 18:47:31 -0400 Subject: [PATCH] AD code in C++ with ROOT compatible --- .gitignore | 3 + Qk.h | 267 +++++++++++++++++++++++++++++++++++++++++++++++ ad++.cpp | 300 +++++++++++++++++++++++++++++++++++++++++++++++++++++ jSymbol.h | 129 +++++++++++++++++++++++ makefile | 2 + 5 files changed, 701 insertions(+) create mode 100644 .gitignore create mode 100644 Qk.h create mode 100644 ad++.cpp create mode 100644 jSymbol.h create mode 100644 makefile diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..7ecc949 --- /dev/null +++ b/.gitignore @@ -0,0 +1,3 @@ +ad++ +testJSymbol +testJSymbol.cpp diff --git a/Qk.h b/Qk.h new file mode 100644 index 0000000..7f392f1 --- /dev/null +++ b/Qk.h @@ -0,0 +1,267 @@ +double TauCal(double Energy_MeV){ + + double E_log = log(Energy_MeV); + double EL1 = E_log; + double EL2 = pow(E_log,2); + double EL3 = pow(E_log,3); + double EL4 = pow(E_log,4); + double EL5 = pow(E_log,5); + double TT = -1.1907 -0.5372*EL1 - 0.0438*EL2 + 0.0218*EL3 + 0.0765*EL4 + 0.0095*EL5; + + return exp(TT); +} + +double LegendreP(int n, double theta){ + if( n == 0 ) return 1; + if( n == 2 ) return (3. * cos(theta) * cos(theta) -1 )/2.; + if( n == 4 ) return (35 * pow( cos(theta), 4) - 30 * pow(cos(theta),2) + 3.) /8.; + + return 0; +} + +double * QK(double Energy_keV, double radius_cm, double distance_cm, double thickness_cm){ + + double E_MeV = Energy_keV/1000; + double Tau = TauCal(E_MeV); + + double alpha = atan( radius_cm / (distance_cm + thickness_cm) ); + double gamma = atan( radius_cm / distance_cm ); + + double sum1 = 0,sum2 = 0,sum3 = 0.; + double sum4 = 0,sum5 = 0,sum6 = 0.; + + double beta1 = 0; + double beta2 = 0; + double A = 0.; + + int div = 1000; + + double delx1 = (alpha)/div; // mrad + double delx2 = (gamma-alpha)/div; + + for(int i = 0; i<=div; i++){ + + int J = i % 2; + if( J == 0 ){ + A = 2.0; + }else{ + A = 4.0; + beta1 = i * delx1; + beta2 = alpha + i * delx2; + } + + if( i == 0 || i == div ) { + A = 1.0; + beta1 = i * delx1; + beta2 = alpha + i * delx2; + } + + double cosb = cos(beta1); + double sinb = sin(beta1); + double ex1 = exp( - 1.0 * Tau * thickness_cm / cosb ); + double term3 = (1-ex1) * sinb * A * delx1; + double term1 = LegendreP(2, beta1) * term3; + double term2 = LegendreP(4, beta1) * term3; + + sum1 += term1; + sum2 += term2; + sum3 += term3; + + cosb = cos(beta2); + sinb = sin(beta2); + double ex2 = exp( -1 * Tau * (radius_cm / sinb - distance_cm /cosb) ); + double term6 = A * (1-ex2) * sinb * delx2; + double term4 = LegendreP(2, beta2) * term6; + double term5 = LegendreP(4, beta2) * term6; + + sum4 = sum4 +term4; + sum5 = sum5 +term5; + sum6 = sum6 +term6; + + //if( i % 75 == 0) printf("%4d | %10.6f, %10.6f %d | %10.6f, %10.6f %10.6f \n", i, beta, A, J, sum1, sum2, sum3); + } + + double ans1 = sum1/3; + double ans2 = sum2/3; + double ans3 = sum3/3; + double ans4 = sum4/3; + double ans5 = sum5/3; + double ans6 = sum6/3; + + double * Qk = new double[2]; + Qk[0] = (ans1+ans4)/(ans3+ans6); + Qk[1] = (ans2+ans5)/(ans3+ans6); + + printf("--------------\n"); + printf(" QD2 = %lf\n",Qk[0]); + printf(" QD4 = %lf\n",Qk[1]); + printf("--------------\n"); + + return Qk; +} + +/// Relic code +double QK2(double Energy, double radius, double distance, double thickness){ + + + double Qkn = 0.; + double E_mev = Energy/1000; + + double E_log = log(E_mev); + double EL1 = E_log; + double EL2 = pow(E_log,2); + double EL3 = EL1*EL2; + double EL4 = pow(EL2,2); + double EL5 = EL4*EL1; + double TT = -1.1907 -0.5372*EL1 - 0.0438*EL2 + 0.0218*EL3 + 0.0765*EL4 + 0.0095*EL5; + double Tau = exp(TT); +// printf("TLN = %lf\n",TT); +// printf("Tau = %lf\n",Tau); + //calulating attenuation angles + + double Z1 = radius / (distance + thickness); + double Z2 = radius / distance; + double alpha = atan(Z1); + double gamma = atan(Z2); + double beta; + double BL = 0.; + double BU = alpha; + double A = 0.; + double delx1 = (BU-BL)/1000; +// printf("alpha = %lf\n",alpha); +// printf("gamma = %lf\n",gamma); +// printf("delx1 = %lf\n",delx1); + double sum1 = 0,sum2 = 0,sum3 = 0.; + double sum4 = 0,sum5 = 0,sum6 = 0.; + double cosb,sinb,secb,cscb,c2,c4,fac1,fac2,ex1,ex2 = 0.; + double term1 = 0,term2 = 0,term3 = 0.; + double term4 = 0,term5 = 0,term6 = 0.; + int J=0; + + int loop_length = 1000; + for(int i = 0; i<=loop_length; i++){ +/* + if(i > 0 and i < loop_length){ + J = i%2; + //printf("\t\ti = %d\nJ=%d\n",i,J); + if(J==0){A=2.; + }else {A=4.;} + beta = BL+i+delx1; + }else{A=.1;beta = BL+i+delx1;} +*/ + if(i != 0){ + if(i != loop_length){ + J = i%2; + if(J==0){ + A = 2.; + }else{ + A=4.; + beta = BL+i*delx1; + } + }else{ + A=1.0; + beta = BL+i*delx1;} + }else{ + A =1.0; + beta = BL+i*delx1; + } + // printf("Beta = %lf\n",beta); + + cosb = cos(beta); + sinb = sin(beta); + secb = 1.0/cosb; + c2 = pow(cosb,2); + c4 = pow(cosb,4); + + fac1 = -1 *Tau *thickness *secb; + + ex1 = exp(fac1); + term1 = 0.5*(3*c2-1)*(1-ex1)*sinb*A*delx1; + term2 = 0.125*A*(35*c4-30*c2+3)*(1-ex1)*sinb*delx1; + term3 = A*(1-ex1)*sinb*delx1; + + sum1 = sum1 +term1; + sum2 = sum2 +term2; + sum3 = sum3 +term3; + + //if( i % 75 == 0) printf("%4d | %10.6f, %10.6f, %d | %10.6f, %10.6f %10.6f \n", i, beta, A, J, sum1, sum2, sum3); + + } + + double ans1 = sum1/3; + double ans2 = sum2/3; + double ans3 = sum3/3; + + //printf("%10.6f, %10.6f %10.6f \n", ans1, ans2, ans3); + + double LB=alpha; + double UB=gamma; + double delx2 = (UB-LB)/1000; + for(int i = 0; i<=loop_length; i++){ +/* + if(i > 0 and i < loop_length){ + J2 = i%2; + //printf("\t\ti = %d\nJ=%d\n",i,J2); + if(J2==0){B=2.; + }else {B=4.;} + beta2 = LB+i+delx2; + }else{B=.1;beta2 = LB+i+delx2;} +*/ + if(i != 0){ + if(i != loop_length){ + J = i%2; + if(J==0){ + A = 2.; + }else{A=4.;beta = LB+i*delx2;} + }else{A=1.0;beta = LB+i*delx2;} + }else{A =1.0;beta = LB+i*delx2;} + // printf("Beta1 = %lf\n",beta); + cosb = cos(beta); + sinb = sin(beta); + secb = 1.0/cosb; + cscb = 1.0/sinb; + c2 = pow(cosb,2); + c4 = pow(cosb,4); + fac2 = -1 *Tau *(radius*cscb -distance*secb); + ex2 = exp(fac2); + term4 = 0.5*A*(3*c2-1)*(1-ex2)*sinb*delx2; + term5 = 0.125*A*(35*c4-30*c2+3)*(1-ex2)*sinb*delx2; + term6 = A*(1-ex2)*sinb*delx2; + sum4 = sum4 +term4; + sum5 = sum5 +term5; + sum6 = sum6 +term6; + } + double ans4=sum4/3; + double ans5=sum5/3; + double ans6=sum6/3; +/* + printf("ans1:%lf\n",ans1*100); + printf("ans2:%lf\n",ans2*100); + printf("ans3:%lf\n",ans3*100); + printf("ans4:%lf\n",ans4*100); + printf("ans5:%lf\n",ans5*100); + printf("ans6:%lf\n",ans6*100); +*/ + double QD2 = (ans1+ans4)/(ans3+ans6); + double QD4 = (ans2+ans5)/(ans3+ans6); + + printf("--------------\n"); + printf(" QD2 = %lf\n",QD2); + printf(" QD4 = %lf\n",QD4); + printf("--------------\n"); + + /* +//Now output a file that contains R, D , T , gamma energy, attentuation coeff, q2 and q4 + ofstream fileo; + fileo.open ("ad.txt"); + fileo << "Radius = " << radius <<" [cm]\n"; + fileo << "Distance = " << distance <<" [cm]\n"; + fileo << "Thickness = " << thickness <<" [cm]\n"; + fileo << "Atten.C = " << Tau <<" [cm^-1]\n"; + fileo << "Gamma_E = " << Energy <<" [KeV]\n"; + fileo << "QD2 = " << QD2 << "\n"; + fileo << "QD4 = " << QD4 << "\n"; + fileo.close(); + */ + return QD2; +} diff --git a/ad++.cpp b/ad++.cpp new file mode 100644 index 0000000..db41150 --- /dev/null +++ b/ad++.cpp @@ -0,0 +1,300 @@ +#include "jSymbol.h" +#include "Qk.h" + +#include +#include +#include +#include +#include +#include +#include +#include + + +#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 deltaDeg; + std::vector 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; + +} diff --git a/jSymbol.h b/jSymbol.h new file mode 100644 index 0000000..b6a4c42 --- /dev/null +++ b/jSymbol.h @@ -0,0 +1,129 @@ +#include +#include +#include + +using namespace std; + +double factorial(double n){ + if( n < 0 ) return -100.; + return (n == 1. || n == 0.) ? 1. : factorial(n-1) * n ; +} + +double CGcoeff(double J, double m, double J1, double m1, double J2, double m2){ + // (J1,m1) + (J2, m2) = (J, m) + + if( m != m1 + m2 ) return 0; + + double Jmin = abs(J1 - J2); + double Jmax = J1+J2; + + if( J < Jmin || Jmax < J ) return 0; + + double s0 = (2*J+1.) * factorial(J+J1-J2) * factorial(J-J1+J2) * factorial(J1+J2-J) / factorial(J+J1+J2 + 1.); + s0 = sqrt(s0); + + double s = factorial(J +m ) * factorial(J -m); + double s1 = factorial(J1+m1) * factorial(J1-m1); + double s2 = factorial(J2+m2) * factorial(J2-m2); + s = sqrt(s * s1 * s2); + + //printf(" s0, s = %f , %f \n", s0, s); + + int kMax = min( min( J1+J2-J, J1 - m1), J2 + m2); + + double CG = 0.; + for( int k = 0; k <= kMax; k++){ + double k1 = factorial(J1+J2-J-k); + double k2 = factorial(J1-m1-k); + double k3 = factorial(J2+m2-k); + double k4 = factorial(J - J2 + m1 +k); + double k5 = factorial(J - J1 - m2 +k); + double temp = pow(-1, k) / (factorial(k) * k1 * k2 * k3 * k4 * k5); + if( k1 == -100. || k2 == -100. || k3 == -100. || k4 == -100. || k5 == -100. ) temp = 0.; + + + //printf(" %d | %.12f | %.12f | %.12f | %.12f | %.12f | %.12f, %f \n", k, k1, k2, k3, k4, k5, temp, factorial(k) ); + CG += temp; + } + + return s0*s*CG; + +} + +double ThreeJSymbol(double J1, double m1, double J2, double m2, double J3, double m3){ + + // ( J1 J2 J3 ) = (-1)^(J1-J2 - m3)/ sqrt(2*J3+1) * CGcoeff(J3, -m3, J1, m1, J2, m2) + // ( m1 m2 m3 ) + + return pow(-1, J1 - J2 - m3)/sqrt(2*J3+1) * CGcoeff(J3, -m3, J1, m1, J2, m2); + +} + +double SixJSymbol(double J1, double J2, double J3, double J4, double J5, double J6){ + + // coupling of j1, j2, j3 to J-J1 + // J1 = j1 + // J2 = j2 + // J3 = j12 = j1 + j2 + // J4 = j3 + // J5 = J = j1 + j2 + j3 + // J6 = j23 = j2 + j3 + + //check triangle condition + if( J3 < abs(J1 - J2 ) || J1 + J2 < J3 ) return 0; + if( J6 < abs(J2 - J4 ) || J2 + J4 < J6 ) return 0; + if( J5 < abs(J1 - J6 ) || J1 + J6 < J5 ) return 0; + if( J5 < abs(J3 - J4 ) || J3 + J4 < J5 ) return 0; + + double sixJ = 0; + + for( float m1 = -J1; m1 <= J1 ; m1 = m1 + 1){ + for( float m2 = -J2; m2 <= J2 ; m2 = m2 + 1){ + for( float m3 = -J3; m3 <= J3 ; m3 = m3 + 1){ + for( float m4 = -J4; m4 <= J4 ; m4 = m4 + 1){ + for( float m5 = -J5; m5 <= J5 ; m5 = m5 + 1){ + for( float m6 = -J6; m6 <= J6 ; m6 = m6 + 1){ + + double f = (J1 - m1) + (J2 - m2) + (J3 - m3) + (J4 - m4) + (J5 - m5) + (J6 - m6); + + double a1 = ThreeJSymbol( J1, -m1, J2, -m2, J3, -m3); // J3 = j12 + double a2 = ThreeJSymbol( J1, m1, J5, -m5, J6, m6); // J5 = j1 + (J6 = j23) + double a3 = ThreeJSymbol( J4, m4, J2, m2, J6, -m6); // J6 = j23 + double a4 = ThreeJSymbol( J4, -m4, J5, m5, J3, m3); // J5 = j3 + j12 + + double a = a1 * a2 * a3 * a4; + //if( a != 0 ) printf("%4.1f %4.1f %4.1f %4.1f %4.1f %4.1f | %f \n", m1, m2, m3, m4, m5, m6, a); + + sixJ += pow(-1, f) * a1 * a2 * a3 * a4; + + } + } + } + } + } + } + + return sixJ; +} + +double NineJSymbol( double J1, double J2, double J3, double J4, double J5, double J6, double J7, double J8, double J9){ + + double gMin = min( min (min( abs(J1 - J2 ), abs(J4 - J5)) , abs( J4 - J6 )) , abs(J7 - J8)); + double gMax = max( max (max( J1+J2, J4+J5), J3+J6), J7+J8); + + //printf(" gMin, gMax = %f %f \n", gMin, gMax); + + double nineJ = 0; + for( float g = gMin; g <= gMax ; g = g + 1){ + double f = pow(-1, 2*g) * (2*g+1); + double s1 = SixJSymbol(J1, J4, J7, J8, J9, g); + if( s1 == 0 ) continue; + double s2 = SixJSymbol(J2, J5, J8, J4, g, J6); + if( s2 == 0 ) continue; + double s3 = SixJSymbol(J3, J6, J9, g, J1, J2); + if( s3 == 0 ) continue; + nineJ += f* s1*s2*s3; + } + + return nineJ; +} diff --git a/makefile b/makefile new file mode 100644 index 0000000..7fccf09 --- /dev/null +++ b/makefile @@ -0,0 +1,2 @@ +ad++ : ad++.cpp Qk.h jSymbol.h + g++ ad++.cpp -o ad++ `root-config --cflags --glibs`