183 lines
4.2 KiB
C++
183 lines
4.2 KiB
C++
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#include "global.h"
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//To compile : g++ AD.cxx -o {Input Executable Name} -lX11
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#include "Coeff.h"
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using namespace std;
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double CG(double j1, double j2, double J, double m1, double m2, double M){
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//recall that j1,m1 + j2,m2 = J,M
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// printf("-----------------\n");
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if(M != m1 + m2) return 0;
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double Jmin = abs(j1 - j2);
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double Jmax = j1+j2;
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if(J < Jmin || Jmax < J) return 0;
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double a0 = (2*J+1.0)*tgamma(J+j1-j2+1) * tgamma(J-j1+j2+1) * tgamma(j1+j2-J+1)/tgamma(J+j1+j2+1.0 +1);
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double A0 = sqrt(a0);
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double a = tgamma(J+M+1) *tgamma(J-M+1);
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double a1= tgamma(j1+m1+1) *tgamma(j1-m1+1);
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double a2= tgamma(j2+m2+1) *tgamma(j2-m2+1);
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double A = sqrt( a * a1 * a2);
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int pmax = min( min(j1+j2-J,j1-m1),j2 + m2);
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double cg = 0.;
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for( int p =0; p<=pmax;p++){
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double p1 = tgamma(j1+j2-J-p+1);
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double p2 = tgamma(j1-m1-p+1);
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double p3 = tgamma(j2+m2-p+1);
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double p4 = tgamma(J -j2 +m1 +p+1);
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double p5 = tgamma(J -j1 -m2 +p+1);
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double t = pow(-1,p)/(tgamma(p+1) * p1 * p2 * p3 * p4 * p5);
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cg += t;
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}
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return A0*A*cg;
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}
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double ThreeJsym(double j1, double m1, double j2, double m2, double j3, double m3){
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//[j1 j2 j3] = (-1)^(j1-j2-m3)/ sqrt(2*j3+1) * CG(j3, -m3, j1, m1, j2, m2)
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//[m1 m2 m3]
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//J,M,j1,m1,j2,m2)
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//return pow(-1,j1 -j2 -m3)/sqrt(2*j3+1)*CG(j3,-m3,j1,m1,j2,m2);
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double threej = pow(-1,j1 -j2 -m3)/sqrt(2*j3+1)*CG(j3,-m3,j1,m1,j2,m2);
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//double threej = pow(-1,j1 -j2 -m3)/sqrt(2*j3+1)*CG(j1,j2,j3,m1,m2,-m3);
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printf("---------\n");
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printf("3J= %lf\n",threej);
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printf("---------\n");
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return threej;
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}
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double SixJsym(double j1, double j2, double j3, double j4, double j5, double j6){
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//--------------------------------------------------------------------------------//
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// The six j symbol describes the coupling between j1 j2 and j3 to J - j1.
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// essentially a triangle of angular momentum rules between these.
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// j1 = j1
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// j2 = j2
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// j3 = j1 + j2
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// j4 = j3
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// j5 = J = j1 + j2 + j3
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// j6 = j2 + j3
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// ----------------------------------------------------------------------------- //
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// the following conditions check the triangle selection rules
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if( j3 < abs(j1 - j2) || j1 + j2 < j3) return 0;
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if( j6 < abs(j2 - j4) || j2 + j4 < j6) return 0;
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if( j5 < abs(j1 - j6) || j1 + j6 < j5) return 0;
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if( j5 < abs(j3 - j4) || j3 + j4 < j5) return 0;
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// now that they have been checked, we can go ahead and calculate sixJ.
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double sixj = 0.0;
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float m1 = -j1;
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float m2 = -j2;
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float m3 = -j3;
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float m4 = -j4;
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float m5 = -j5;
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float m6 = -j6;
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printf("here\n");
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for(; m1 <= j1; m1 = m1 +1){
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for(; m2 <= j2; m2 = m2 +1){
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for(; m3 <= j3; m3 = m3 + 1){
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for(; m4 <= j4; m4 = m4 +1){
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for(; m5 <= j5; m5 = m5 + 1){
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for(; m6 <= j6; m6 = m6 +1){
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double h = (j1 - m1) + (j2 - m2) + (j3 -m3) + (j4 - m4) + (j5 - m5) + (j6 - m6);
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double b1 = ThreeJsym(j1, -m1, j2, -m2, j3, -m3);
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double b2 = ThreeJsym(j1, m1, j5, -m5, j6, m6);
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double b3 = ThreeJsym(j4, m4, j2, m2, j6, -m6);
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double b4 = ThreeJsym(j4, -m4, j5, m5, j3, m3);
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double b = b1 * b2 * b3 * b4;
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printf("h = %lf\n", h);
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printf("b1 = %lf\n", b1);
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printf("b2 = %lf\n", b2);
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printf("b3 = %lf\n", b3);
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printf("b4 = %lf\n", b4);
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printf("b = %lf\n", b);
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sixj += pow(-1,h)*b;
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}
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}
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}
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}
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}
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}
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return sixj;
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}
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int main(int argc, char ** argv){
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//if mod (2*J1,2) = 1 do this
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// double A0[6] = {1,1,2,0,0,0};
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// double A1[6] = {1,1,4,0,0,0};
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//if mod(2*j1,20 = 0 do this
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double j1 = 1.;
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double j2 = 2.;
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double A0[6] = {j1,j1,2,.5,-.5,0};
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double A1[6] = {j1,j1,2,-.5,.5,0};
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double A2[6] = {j1,j1,4,-.5,.5,0};
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double A3[6] = {j1,j1,4,.5,-.5,0};
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double cgr0= CG(j1,j1,2,.5,-.5,0);
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double cgr1= CG(j1,j1,2,-.5,.5,0);
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double cgr2= CG(j1,j1,4,.5,-.5,0);
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double cgr3= CG(j1,j1,4,-.5,.5,0);
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printf("------\n");
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// printf("CGR0 = %lf\n",cgr0);
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// printf("CGR1 = %lf\n",cgr1);
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// printf("CGR2 = %lf\n",cgr2);
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// printf("CGR3 = %lf\n",cgr3);
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double sixj = SixJsym(j1,j1,1.,1.,2.,2.);
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double sixj2 = SixJsym(j1,j1,1.,2.,2.,2.);
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double sixj3 = SixJsym(j1,j1,2.,2.,2.,2.);
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printf("6-J = %lf\n", sixj);
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return 0;
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}
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