/* The functions in this file contain the generators of su(3)
   in the fundamental representation (Gell-Mann matrices). */

#include <su3.h>


/* The function gell_mann_mat() returns the 8 Gell-Mann matrices,
   a = 1,...,8. */

su3_mat gell_mann_mat(int a)
{
     su3_mat gen;

     switch(a)
     {
     case 1:
           {
           gen.su3m[1][1] = Complex(0., 0.);
           gen.su3m[1][2] = Complex(1., 0.);
           gen.su3m[1][3] = Complex(0., 0.);
           gen.su3m[2][1] = Complex(1., 0.);
           gen.su3m[2][2] = Complex(0., 0.);
           gen.su3m[2][3] = Complex(0., 0.);
           gen.su3m[3][1] = Complex(0., 0.);
           gen.su3m[3][2] = Complex(0., 0.);
           gen.su3m[3][3] = Complex(0., 0.);

           break;
           }
     case 2:
           {
           gen.su3m[1][1] = Complex(0., 0.);
           gen.su3m[1][2] = Complex(0., -1.);
           gen.su3m[1][3] = Complex(0., 0.);
           gen.su3m[2][1] = Complex(0., 1.);
           gen.su3m[2][2] = Complex(0., 0.);
           gen.su3m[2][3] = Complex(0., 0.);
           gen.su3m[3][1] = Complex(0., 0.);
           gen.su3m[3][2] = Complex(0., 0.);
           gen.su3m[3][3] = Complex(0., 0.);

           break;
           }
     case 3:
           {
           gen.su3m[1][1] = Complex(1., 0.);
           gen.su3m[1][2] = Complex(0., 0.);
           gen.su3m[1][3] = Complex(0., 0.);
           gen.su3m[2][1] = Complex(0., 0.);
           gen.su3m[2][2] = Complex(-1., 0.);
           gen.su3m[2][3] = Complex(0., 0.);
           gen.su3m[3][1] = Complex(0., 0.);
           gen.su3m[3][2] = Complex(0., 0.);
           gen.su3m[3][3] = Complex(0., 0.);

           break;
           }
     case 4:
           {
           gen.su3m[1][1] = Complex(0., 0.);
           gen.su3m[1][2] = Complex(0., 0.);
           gen.su3m[1][3] = Complex(1., 0.);
           gen.su3m[2][1] = Complex(0., 0.);
           gen.su3m[2][2] = Complex(0., 0.);
           gen.su3m[2][3] = Complex(0., 0.);
           gen.su3m[3][1] = Complex(1., 0.);
           gen.su3m[3][2] = Complex(0., 0.);
           gen.su3m[3][3] = Complex(0., 0.);

           break;
           }
     case 5:
           {
           gen.su3m[1][1] = Complex(0., 0.);
           gen.su3m[1][2] = Complex(0., 0.);
           gen.su3m[1][3] = Complex(0., -1.);
           gen.su3m[2][1] = Complex(0., 0.);
           gen.su3m[2][2] = Complex(0., 0.);
           gen.su3m[2][3] = Complex(0., 0.);
           gen.su3m[3][1] = Complex(0., 1.);
           gen.su3m[3][2] = Complex(0., 0.);
           gen.su3m[3][3] = Complex(0., 0.);

           break;
           }
     case 6:
           {
           gen.su3m[1][1] = Complex(0., 0.);
           gen.su3m[1][2] = Complex(0., 0.);
           gen.su3m[1][3] = Complex(0., 0.);
           gen.su3m[2][1] = Complex(0., 0.);
           gen.su3m[2][2] = Complex(0., 0.);
           gen.su3m[2][3] = Complex(1., 0.);
           gen.su3m[3][1] = Complex(0., 0.);
           gen.su3m[3][2] = Complex(1., 0.);
           gen.su3m[3][3] = Complex(0., 0.);

           break;
           }
     case 7:
           {
           gen.su3m[1][1] = Complex(0., 0.);
           gen.su3m[1][2] = Complex(0., 0.);
           gen.su3m[1][3] = Complex(0., 0.);
           gen.su3m[2][1] = Complex(0., 0.);
           gen.su3m[2][2] = Complex(0., 0.);
           gen.su3m[2][3] = Complex(0., -1.);
           gen.su3m[3][1] = Complex(0., 0.);
           gen.su3m[3][2] = Complex(0., 1.);
           gen.su3m[3][3] = Complex(0., 0.);

           break;
           }
     case 8:
           {
           gen.su3m[1][1] = Complex(1./sqrt(3.), 0.);
           gen.su3m[1][2] = Complex(0., 0.);
           gen.su3m[1][3] = Complex(0., 0.);
           gen.su3m[2][1] = Complex(0., 0.);
           gen.su3m[2][2] = Complex(1./sqrt(3.), 0.);
           gen.su3m[2][3] = Complex(0., 0.);
           gen.su3m[3][1] = Complex(0., 0.);
           gen.su3m[3][2] = Complex(0., 0.);
           gen.su3m[3][3] = Complex(-2./sqrt(3.), 0.);

           break;
           }
     }
           return gen;
}  


su3_mat su3_mul(su3_mat a, su3_mat b)
{
     su3_mat c;
     int i, j;

     for(i = 1; i <= 3; i++)
     {
        for(j = 1; j <= 3; j++)
        {
	   int k;
	   dcomplex temp = Complex(0., 0.);
 
           for(k = 1; k <= 3; k++)
           {	   
           temp = Cadd(temp, Cmul(a.su3m[i][k], b.su3m[k][j]) );
	   }
	   
           c.su3m[i][j] = temp;
	 }
     }
     return c;
}