OFF axis wilson loops calculations using SIMULATeQCD

The x_y exchange and mu_nu exhange is giving same results for the off axis wilson loops, but is not matching for x==y or y==z or x==z or x==y==z. For these cases, we can take average over the two paths for same \(R=\sqrt{x^2+y^2+z^2}\) or just leave it as it might not change the potential and pseudo potentials and string tensions.

The planer wilson loops are matching with MILC results, in order to check the off axis wilson loops, I have created two algorithms ,

  1. two dimensional bresenham algorithm
  2. three dimensional bresenham algorithms

The two dimensional bresenham algorithm is used to calculate the off axis wilson loops in the 2D space and 1d space/time, while the three dimensional bresenham algorithm is used to calculate the off axis wilson loops in the 4D space-time.

The results from 2d case shall be able to obtained from the 3d case.

The results from 2d case also varies with the following funciton calling:

  1. case 3: for(nu=1;nu<3;nu++)
    		{
    			for(mu=0;mu<nu;mu++)
    			{ 
    				temp1=BresenhamLoopXYL_2d(_x,_y,_z,site,mu,nu,_ex_dir);
    				temp2=BresenhamLoopXYU_2d(_x,_y,_z,site,mu,nu,_ex_dir);
    				result+=tr_d(temp1*dagger(temp2));
    		//replacing x<->y
    				/* temp1=BresenhamLoopXYL_2d(_y,_x,_z,site,mu,nu,_ex_dir); */
    				/* temp2=BresenhamLoopXYU_2d(_y,_x,_z,site,mu,nu,_ex_dir); */
    				temp1=BresenhamLoopXYL_2d(_x,_y,_z,site,nu,mu,_ex_dir);
    				temp2=BresenhamLoopXYU_2d(_x,_y,_z,site,nu,mu,_ex_dir);
    				result+=tr_d(temp1*dagger(temp2));
    			}
    		}
    		return result/6.0;
    		break;
    
    

2.

case 3: for(nu=1;nu<3;nu++)
		{
			for(mu=0;mu<nu;mu++)
			{ 
				temp1=BresenhamLoopXYL_2d(_x,_y,_z,site,mu,nu,_ex_dir);
				temp2=BresenhamLoopXYU_2d(_x,_y,_z,site,mu,nu,_ex_dir);
				result+=tr_d(temp1*dagger(temp2));
		//replacing x<->y
				temp1=BresenhamLoopXYL_2d(_y,_x,_z,site,mu,nu,_ex_dir);
				temp2=BresenhamLoopXYU_2d(_y,_x,_z,site,mu,nu,_ex_dir);
				/* temp1=BresenhamLoopXYL_2d(_x,_y,_z,site,nu,mu,_ex_dir); */
				/* temp2=BresenhamLoopXYU_2d(_x,_y,_z,site,nu,mu,_ex_dir); */
				result+=tr_d(temp1*dagger(temp2));
			}
		}
		return result/6.0;
		break;

The first one just changes the directions but the second one swapes the x and y coordinates.

Results from 1st case: (changing directions)

Node:0,Smear_count:0,x=0,y=1,Length=1.000000,Height=1,ex_dir=3,Wilson Loop:5.415310497463935e-01
Node:0,Smear_count:0,x=0,y=1,Length=1.000000,Height=2,ex_dir=3,Wilson Loop:2.989843084939524e-01
Node:0,Smear_count:0,x=0,y=1,Length=1.000000,Height=3,ex_dir=3,Wilson Loop:1.683720211814673e-01
Node:0,Smear_count:0,x=0,y=1,Length=1.000000,Height=4,ex_dir=3,Wilson Loop:9.513755112092502e-02
Node:0,Smear_count:0,x=0,y=2,Length=2.000000,Height=1,ex_dir=3,Wilson Loop:2.988292105397755e-01
Node:0,Smear_count:0,x=0,y=2,Length=2.000000,Height=2,ex_dir=3,Wilson Loop:1.036251536262440e-01
Node:0,Smear_count:0,x=0,y=2,Length=2.000000,Height=3,ex_dir=3,Wilson Loop:3.934422556804130e-02
Node:0,Smear_count:0,x=0,y=2,Length=2.000000,Height=4,ex_dir=3,Wilson Loop:1.534567048782771e-02
Node:0,Smear_count:0,x=0,y=3,Length=3.000000,Height=1,ex_dir=3,Wilson Loop:1.683097768375253e-01
Node:0,Smear_count:0,x=0,y=3,Length=3.000000,Height=2,ex_dir=3,Wilson Loop:3.952744879497768e-02
Node:0,Smear_count:0,x=0,y=3,Length=3.000000,Height=3,ex_dir=3,Wilson Loop:1.129745493249806e-02
Node:0,Smear_count:0,x=0,y=3,Length=3.000000,Height=4,ex_dir=3,Wilson Loop:3.495959058142938e-03
Node:0,Smear_count:0,x=0,y=4,Length=4.000000,Height=1,ex_dir=3,Wilson Loop:9.509986024471435e-02
Node:0,Smear_count:0,x=0,y=4,Length=4.000000,Height=2,ex_dir=3,Wilson Loop:1.532669443767490e-02
Node:0,Smear_count:0,x=0,y=4,Length=4.000000,Height=3,ex_dir=3,Wilson Loop:3.419764739416865e-03
Node:0,Smear_count:0,x=0,y=4,Length=4.000000,Height=4,ex_dir=3,Wilson Loop:7.796308238129630e-04
Node:0,Smear_count:0,x=1,y=1,Length=1.414214,Height=1,ex_dir=3,Wilson Loop:3.479741961411804e-01
Node:0,Smear_count:0,x=1,y=1,Length=1.414214,Height=2,ex_dir=3,Wilson Loop:1.453837667666475e-01
Node:0,Smear_count:0,x=1,y=1,Length=1.414214,Height=3,ex_dir=3,Wilson Loop:6.563371464165794e-02
Node:0,Smear_count:0,x=1,y=1,Length=1.414214,Height=4,ex_dir=3,Wilson Loop:3.017105852160809e-02
Node:0,Smear_count:0,x=1,y=2,Length=2.236068,Height=1,ex_dir=3,Wilson Loop:2.207222968648315e-01
Node:0,Smear_count:0,x=1,y=2,Length=2.236068,Height=2,ex_dir=3,Wilson Loop:6.792344696820346e-02
Node:0,Smear_count:0,x=1,y=2,Length=2.236068,Height=3,ex_dir=3,Wilson Loop:2.394174427484879e-02
Node:0,Smear_count:0,x=1,y=2,Length=2.236068,Height=4,ex_dir=3,Wilson Loop:8.737576050305213e-03
Node:0,Smear_count:0,x=1,y=3,Length=3.162278,Height=1,ex_dir=3,Wilson Loop:1.269590315734095e-01
Node:0,Smear_count:0,x=1,y=3,Length=3.162278,Height=2,ex_dir=3,Wilson Loop:2.751369434715729e-02
Node:0,Smear_count:0,x=1,y=3,Length=3.162278,Height=3,ex_dir=3,Wilson Loop:7.528610445847035e-03
Node:0,Smear_count:0,x=1,y=3,Length=3.162278,Height=4,ex_dir=3,Wilson Loop:2.275467219509008e-03
Node:0,Smear_count:0,x=1,y=4,Length=4.123106,Height=1,ex_dir=3,Wilson Loop:7.302148572342397e-02
Node:0,Smear_count:0,x=1,y=4,Length=4.123106,Height=2,ex_dir=3,Wilson Loop:1.119225959266536e-02
Node:0,Smear_count:0,x=1,y=4,Length=4.123106,Height=3,ex_dir=3,Wilson Loop:2.408397375147882e-03
Node:0,Smear_count:0,x=1,y=4,Length=4.123106,Height=4,ex_dir=3,Wilson Loop:4.720684023649508e-04
Node:0,Smear_count:0,x=2,y=2,Length=2.828427,Height=1,ex_dir=3,Wilson Loop:1.421079996197134e-01
Node:0,Smear_count:0,x=2,y=2,Length=2.828427,Height=2,ex_dir=3,Wilson Loop:3.385622608208851e-02
Node:0,Smear_count:0,x=2,y=2,Length=2.828427,Height=3,ex_dir=3,Wilson Loop:1.015315988776403e-02
Node:0,Smear_count:0,x=2,y=2,Length=2.828427,Height=4,ex_dir=3,Wilson Loop:3.190247666421482e-03
Node:0,Smear_count:0,x=2,y=3,Length=3.605551,Height=1,ex_dir=3,Wilson Loop:8.468717998213722e-02
Node:0,Smear_count:0,x=2,y=3,Length=3.605551,Height=2,ex_dir=3,Wilson Loop:1.528402673868381e-02
Node:0,Smear_count:0,x=2,y=3,Length=3.605551,Height=3,ex_dir=3,Wilson Loop:3.691426209264199e-03
Node:0,Smear_count:0,x=2,y=3,Length=3.605551,Height=4,ex_dir=3,Wilson Loop:8.774445386751247e-04
Node:0,Smear_count:0,x=2,y=4,Length=4.472136,Height=1,ex_dir=3,Wilson Loop:5.393557100198080e-02
Node:0,Smear_count:0,x=2,y=4,Length=4.472136,Height=2,ex_dir=3,Wilson Loop:7.246089970549818e-03
Node:0,Smear_count:0,x=2,y=4,Length=4.472136,Height=3,ex_dir=3,Wilson Loop:1.538623074674748e-03
Node:0,Smear_count:0,x=2,y=4,Length=4.472136,Height=4,ex_dir=3,Wilson Loop:3.492485230801360e-04
Node:0,Smear_count:0,x=3,y=3,Length=4.242641,Height=1,ex_dir=3,Wilson Loop:5.887790283320022e-02
Node:0,Smear_count:0,x=3,y=3,Length=4.242641,Height=2,ex_dir=3,Wilson Loop:8.428507072353165e-03
Node:0,Smear_count:0,x=3,y=3,Length=4.242641,Height=3,ex_dir=3,Wilson Loop:1.813602914510841e-03
Node:0,Smear_count:0,x=3,y=3,Length=4.242641,Height=4,ex_dir=3,Wilson Loop:3.298736519044532e-04
Node:0,Smear_count:0,x=3,y=4,Length=5.000000,Height=1,ex_dir=3,Wilson Loop:3.519563294174048e-02
Node:0,Smear_count:0,x=3,y=4,Length=5.000000,Height=2,ex_dir=3,Wilson Loop:3.789589670139042e-03
Node:0,Smear_count:0,x=3,y=4,Length=5.000000,Height=3,ex_dir=3,Wilson Loop:7.511445102987512e-04
Node:0,Smear_count:0,x=3,y=4,Length=5.000000,Height=4,ex_dir=3,Wilson Loop:2.194875653005857e-04
Node:0,Smear_count:0,x=4,y=4,Length=5.656854,Height=1,ex_dir=3,Wilson Loop:2.449969910992774e-02
Node:0,Smear_count:0,x=4,y=4,Length=5.656854,Height=2,ex_dir=3,Wilson Loop:2.259314389388597e-03
Node:0,Smear_count:0,x=4,y=4,Length=5.656854,Height=3,ex_dir=3,Wilson Loop:3.949639229747959e-04
Node:0,Smear_count:0,x=4,y=4,Length=5.656854,Height=4,ex_dir=3,Wilson Loop:4.821896331187788e-05
2d bresenham results end here
Node:0,Smear_count:0,Length=1.000000,Height=1,ex_dir=3,Wilson Loop:5.415310497463935e-01
Node:0,Smear_count:0,Length=1.000000,Height=2,ex_dir=3,Wilson Loop:2.989843084939524e-01
Node:0,Smear_count:0,Length=1.000000,Height=3,ex_dir=3,Wilson Loop:1.683720211814673e-01
Node:0,Smear_count:0,Length=1.000000,Height=4,ex_dir=3,Wilson Loop:9.513755112092502e-02
Node:0,Smear_count:0,Length=2.000000,Height=1,ex_dir=3,Wilson Loop:2.988292105397755e-01
Node:0,Smear_count:0,Length=2.000000,Height=2,ex_dir=3,Wilson Loop:1.036251536262440e-01
Node:0,Smear_count:0,Length=2.000000,Height=3,ex_dir=3,Wilson Loop:3.934422556804130e-02
Node:0,Smear_count:0,Length=2.000000,Height=4,ex_dir=3,Wilson Loop:1.534567048782771e-02
Node:0,Smear_count:0,Length=3.000000,Height=1,ex_dir=3,Wilson Loop:1.683097768375253e-01
Node:0,Smear_count:0,Length=3.000000,Height=2,ex_dir=3,Wilson Loop:3.952744879497768e-02
Node:0,Smear_count:0,Length=3.000000,Height=3,ex_dir=3,Wilson Loop:1.129745493249806e-02
Node:0,Smear_count:0,Length=3.000000,Height=4,ex_dir=3,Wilson Loop:3.495959058142938e-03
Node:0,Smear_count:0,Length=4.000000,Height=1,ex_dir=3,Wilson Loop:9.509986024471435e-02
Node:0,Smear_count:0,Length=4.000000,Height=2,ex_dir=3,Wilson Loop:1.532669443767490e-02
Node:0,Smear_count:0,Length=4.000000,Height=3,ex_dir=3,Wilson Loop:3.419764739416865e-03
Node:0,Smear_count:0,Length=4.000000,Height=4,ex_dir=3,Wilson Loop:7.796308238129630e-04
Node:0,Smear_count:0,Length=1.414214,Height=1,ex_dir=3,Wilson Loop:3.478524630355460e-01
Node:0,Smear_count:0,Length=1.414214,Height=2,ex_dir=3,Wilson Loop:1.452627579620166e-01
Node:0,Smear_count:0,Length=1.414214,Height=3,ex_dir=3,Wilson Loop:6.560547922366472e-02
Node:0,Smear_count:0,Length=1.414214,Height=4,ex_dir=3,Wilson Loop:3.006449758343626e-02
Node:0,Smear_count:0,Length=2.236068,Height=1,ex_dir=3,Wilson Loop:2.207222968648315e-01
Node:0,Smear_count:0,Length=2.236068,Height=2,ex_dir=3,Wilson Loop:6.792344696820346e-02
Node:0,Smear_count:0,Length=2.236068,Height=3,ex_dir=3,Wilson Loop:2.394174427484879e-02
Node:0,Smear_count:0,Length=2.236068,Height=4,ex_dir=3,Wilson Loop:8.737576050305213e-03
Node:0,Smear_count:0,Length=3.162278,Height=1,ex_dir=3,Wilson Loop:1.269590315734095e-01
Node:0,Smear_count:0,Length=3.162278,Height=2,ex_dir=3,Wilson Loop:2.751369434715729e-02
Node:0,Smear_count:0,Length=3.162278,Height=3,ex_dir=3,Wilson Loop:7.528610445847035e-03
Node:0,Smear_count:0,Length=3.162278,Height=4,ex_dir=3,Wilson Loop:2.275467219509008e-03
Node:0,Smear_count:0,Length=4.123106,Height=1,ex_dir=3,Wilson Loop:7.302148572342397e-02
Node:0,Smear_count:0,Length=4.123106,Height=2,ex_dir=3,Wilson Loop:1.119225959266536e-02
Node:0,Smear_count:0,Length=4.123106,Height=3,ex_dir=3,Wilson Loop:2.408397375147882e-03
Node:0,Smear_count:0,Length=4.123106,Height=4,ex_dir=3,Wilson Loop:4.720684023649508e-04
Node:0,Smear_count:0,Length=2.828427,Height=1,ex_dir=3,Wilson Loop:1.419193153520172e-01
Node:0,Smear_count:0,Length=2.828427,Height=2,ex_dir=3,Wilson Loop:3.370156398488239e-02
Node:0,Smear_count:0,Length=2.828427,Height=3,ex_dir=3,Wilson Loop:1.020813369097898e-02
Node:0,Smear_count:0,Length=2.828427,Height=4,ex_dir=3,Wilson Loop:3.110595408555808e-03
Node:0,Smear_count:0,Length=3.605551,Height=1,ex_dir=3,Wilson Loop:8.468717998213722e-02
Node:0,Smear_count:0,Length=3.605551,Height=2,ex_dir=3,Wilson Loop:1.528402673868381e-02
Node:0,Smear_count:0,Length=3.605551,Height=3,ex_dir=3,Wilson Loop:3.691426209264199e-03
Node:0,Smear_count:0,Length=3.605551,Height=4,ex_dir=3,Wilson Loop:8.774445386751247e-04
Node:0,Smear_count:0,Length=4.472136,Height=1,ex_dir=3,Wilson Loop:5.393557100198080e-02
Node:0,Smear_count:0,Length=4.472136,Height=2,ex_dir=3,Wilson Loop:7.246089970549817e-03
Node:0,Smear_count:0,Length=4.472136,Height=3,ex_dir=3,Wilson Loop:1.538623074674748e-03
Node:0,Smear_count:0,Length=4.472136,Height=4,ex_dir=3,Wilson Loop:3.492485230801360e-04
Node:0,Smear_count:0,Length=4.242641,Height=1,ex_dir=3,Wilson Loop:5.886688277777838e-02
Node:0,Smear_count:0,Length=4.242641,Height=2,ex_dir=3,Wilson Loop:8.357088014724416e-03
Node:0,Smear_count:0,Length=4.242641,Height=3,ex_dir=3,Wilson Loop:1.823944477897913e-03
Node:0,Smear_count:0,Length=4.242641,Height=4,ex_dir=3,Wilson Loop:2.885129031228969e-04
Node:0,Smear_count:0,Length=5.000000,Height=1,ex_dir=3,Wilson Loop:3.519563294174048e-02
Node:0,Smear_count:0,Length=5.000000,Height=2,ex_dir=3,Wilson Loop:3.789589670139042e-03
Node:0,Smear_count:0,Length=5.000000,Height=3,ex_dir=3,Wilson Loop:7.511445102987512e-04
Node:0,Smear_count:0,Length=5.000000,Height=4,ex_dir=3,Wilson Loop:2.194875653005858e-04
Node:0,Smear_count:0,Length=5.656854,Height=1,ex_dir=3,Wilson Loop:2.460185528998115e-02
Node:0,Smear_count:0,Length=5.656854,Height=2,ex_dir=3,Wilson Loop:2.280548448069865e-03
Node:0,Smear_count:0,Length=5.656854,Height=3,ex_dir=3,Wilson Loop:2.454432334364802e-04
Node:0,Smear_count:0,Length=5.656854,Height=4,ex_dir=3,Wilson Loop:-1.417845523514047e-04
Node:0,Smear_count:0,Length=1.732051,Height=1,ex_dir=3,Wilson Loop:2.323584539802566e-01
Node:0,Smear_count:0,Length=1.732051,Height=2,ex_dir=3,Wilson Loop:8.006702113996193e-02
Node:0,Smear_count:0,Length=1.732051,Height=3,ex_dir=3,Wilson Loop:3.181405632272664e-02
Node:0,Smear_count:0,Length=1.732051,Height=4,ex_dir=3,Wilson Loop:1.326117286861066e-02
Node:0,Smear_count:0,Length=2.449490,Height=1,ex_dir=3,Wilson Loop:1.538339706597785e-01
Node:0,Smear_count:0,Length=2.449490,Height=2,ex_dir=3,Wilson Loop:4.184440696907019e-02
Node:0,Smear_count:0,Length=2.449490,Height=3,ex_dir=3,Wilson Loop:1.391336201023652e-02
Node:0,Smear_count:0,Length=2.449490,Height=4,ex_dir=3,Wilson Loop:4.910984299235446e-03
Node:0,Smear_count:0,Length=3.316625,Height=1,ex_dir=3,Wilson Loop:8.942348744270423e-02
Node:0,Smear_count:0,Length=3.316625,Height=2,ex_dir=3,Wilson Loop:1.759755462346386e-02
Node:0,Smear_count:0,Length=3.316625,Height=3,ex_dir=3,Wilson Loop:4.846163955699981e-03
Node:0,Smear_count:0,Length=3.316625,Height=4,ex_dir=3,Wilson Loop:1.327808488575193e-03
Node:0,Smear_count:0,Length=4.242641,Height=1,ex_dir=3,Wilson Loop:5.191201830929035e-02
Node:0,Smear_count:0,Length=4.242641,Height=2,ex_dir=3,Wilson Loop:7.402214117360789e-03
Node:0,Smear_count:0,Length=4.242641,Height=3,ex_dir=3,Wilson Loop:1.717061134984803e-03
Node:0,Smear_count:0,Length=4.242641,Height=4,ex_dir=3,Wilson Loop:2.938044918773427e-04
Node:0,Smear_count:0,Length=3.000000,Height=1,ex_dir=3,Wilson Loop:9.930589878310135e-02
Node:0,Smear_count:0,Length=3.000000,Height=2,ex_dir=3,Wilson Loop:2.108975197267152e-02
Node:0,Smear_count:0,Length=3.000000,Height=3,ex_dir=3,Wilson Loop:6.009538254694365e-03
Node:0,Smear_count:0,Length=3.000000,Height=4,ex_dir=3,Wilson Loop:1.905836071580671e-03
Node:0,Smear_count:0,Length=3.741657,Height=1,ex_dir=3,Wilson Loop:6.438079130095083e-02
Node:0,Smear_count:0,Length=3.741657,Height=2,ex_dir=3,Wilson Loop:1.082060495845360e-02
Node:0,Smear_count:0,Length=3.741657,Height=3,ex_dir=3,Wilson Loop:2.672380238997035e-03
Node:0,Smear_count:0,Length=3.741657,Height=4,ex_dir=3,Wilson Loop:5.786291189731613e-04
Node:0,Smear_count:0,Length=4.582576,Height=1,ex_dir=3,Wilson Loop:4.125809978356904e-02
Node:0,Smear_count:0,Length=4.582576,Height=2,ex_dir=3,Wilson Loop:5.282381720655011e-03
Node:0,Smear_count:0,Length=4.582576,Height=3,ex_dir=3,Wilson Loop:1.164736883703600e-03
Node:0,Smear_count:0,Length=4.582576,Height=4,ex_dir=3,Wilson Loop:3.784746336948503e-04
Node:0,Smear_count:0,Length=4.358899,Height=1,ex_dir=3,Wilson Loop:4.255546582420177e-02
Node:0,Smear_count:0,Length=4.358899,Height=2,ex_dir=3,Wilson Loop:5.876139287874373e-03
Node:0,Smear_count:0,Length=4.358899,Height=3,ex_dir=3,Wilson Loop:1.034933492545645e-03
Node:0,Smear_count:0,Length=4.358899,Height=4,ex_dir=3,Wilson Loop:3.295591040450346e-04
Node:0,Smear_count:0,Length=5.099020,Height=1,ex_dir=3,Wilson Loop:2.555698326039416e-02
Node:0,Smear_count:0,Length=5.099020,Height=2,ex_dir=3,Wilson Loop:2.529803294191246e-03
Node:0,Smear_count:0,Length=5.099020,Height=3,ex_dir=3,Wilson Loop:4.281796021541677e-04
Node:0,Smear_count:0,Length=5.099020,Height=4,ex_dir=3,Wilson Loop:-1.562759680586854e-04
Node:0,Smear_count:0,Length=5.744563,Height=1,ex_dir=3,Wilson Loop:1.770978858540991e-02
Node:0,Smear_count:0,Length=5.744563,Height=2,ex_dir=3,Wilson Loop:1.468039965800867e-03
Node:0,Smear_count:0,Length=5.744563,Height=3,ex_dir=3,Wilson Loop:1.476326890372761e-04
Node:0,Smear_count:0,Length=5.744563,Height=4,ex_dir=3,Wilson Loop:9.665946952860879e-05
Node:0,Smear_count:0,Length=3.464102,Height=1,ex_dir=3,Wilson Loop:6.779105621515683e-02
Node:0,Smear_count:0,Length=3.464102,Height=2,ex_dir=3,Wilson Loop:1.273369956560854e-02
Node:0,Smear_count:0,Length=3.464102,Height=3,ex_dir=3,Wilson Loop:3.272078383851460e-03
Node:0,Smear_count:0,Length=3.464102,Height=4,ex_dir=3,Wilson Loop:5.980228416986084e-04
Node:0,Smear_count:0,Length=4.123106,Height=1,ex_dir=3,Wilson Loop:4.058556454825119e-02
Node:0,Smear_count:0,Length=4.123106,Height=2,ex_dir=3,Wilson Loop:5.661245822911845e-03
Node:0,Smear_count:0,Length=4.123106,Height=3,ex_dir=3,Wilson Loop:1.234203128978552e-03
Node:0,Smear_count:0,Length=4.123106,Height=4,ex_dir=3,Wilson Loop:3.388239801386483e-04
Node:0,Smear_count:0,Length=4.898979,Height=1,ex_dir=3,Wilson Loop:2.696368273734452e-02
Node:0,Smear_count:0,Length=4.898979,Height=2,ex_dir=3,Wilson Loop:3.234845276883074e-03
Node:0,Smear_count:0,Length=4.898979,Height=3,ex_dir=3,Wilson Loop:6.524998016982003e-04
Node:0,Smear_count:0,Length=4.898979,Height=4,ex_dir=3,Wilson Loop:1.579026491889378e-04
Node:0,Smear_count:0,Length=4.690416,Height=1,ex_dir=3,Wilson Loop:2.884943229379707e-02
Node:0,Smear_count:0,Length=4.690416,Height=2,ex_dir=3,Wilson Loop:3.178057484687282e-03
Node:0,Smear_count:0,Length=4.690416,Height=3,ex_dir=3,Wilson Loop:5.031258828212734e-04
Node:0,Smear_count:0,Length=4.690416,Height=4,ex_dir=3,Wilson Loop:1.317989831511726e-04
Node:0,Smear_count:0,Length=5.385165,Height=1,ex_dir=3,Wilson Loop:1.903957899548749e-02
Node:0,Smear_count:0,Length=5.385165,Height=2,ex_dir=3,Wilson Loop:1.679988583422119e-03
Node:0,Smear_count:0,Length=5.385165,Height=3,ex_dir=3,Wilson Loop:3.437611241726383e-04
Node:0,Smear_count:0,Length=5.385165,Height=4,ex_dir=3,Wilson Loop:5.166813119514661e-05
Node:0,Smear_count:0,Length=6.000000,Height=1,ex_dir=3,Wilson Loop:1.233987120927505e-02
Node:0,Smear_count:0,Length=6.000000,Height=2,ex_dir=3,Wilson Loop:8.043048675692978e-04
Node:0,Smear_count:0,Length=6.000000,Height=3,ex_dir=3,Wilson Loop:2.323050121998040e-04
Node:0,Smear_count:0,Length=6.000000,Height=4,ex_dir=3,Wilson Loop:2.840353268904505e-04
Node:0,Smear_count:0,Length=5.196152,Height=1,ex_dir=3,Wilson Loop:1.992332552753873e-02
Node:0,Smear_count:0,Length=5.196152,Height=2,ex_dir=3,Wilson Loop:2.079031655675860e-03
Node:0,Smear_count:0,Length=5.196152,Height=3,ex_dir=3,Wilson Loop:1.755339643704426e-04
Node:0,Smear_count:0,Length=5.196152,Height=4,ex_dir=3,Wilson Loop:-2.936127237526064e-04
Node:0,Smear_count:0,Length=5.830952,Height=1,ex_dir=3,Wilson Loop:1.221350507302980e-02
Node:0,Smear_count:0,Length=5.830952,Height=2,ex_dir=3,Wilson Loop:8.044403437736970e-04
Node:0,Smear_count:0,Length=5.830952,Height=3,ex_dir=3,Wilson Loop:-1.406735385787728e-04
Node:0,Smear_count:0,Length=5.830952,Height=4,ex_dir=3,Wilson Loop:3.238427416860720e-04
Node:0,Smear_count:0,Length=6.403124,Height=1,ex_dir=3,Wilson Loop:8.495988381667964e-03
Node:0,Smear_count:0,Length=6.403124,Height=2,ex_dir=3,Wilson Loop:6.750722530508155e-04
Node:0,Smear_count:0,Length=6.403124,Height=3,ex_dir=3,Wilson Loop:5.838194704659824e-05
Node:0,Smear_count:0,Length=6.403124,Height=4,ex_dir=3,Wilson Loop:3.014625642239870e-05
Node:0,Smear_count:0,Length=6.928203,Height=1,ex_dir=3,Wilson Loop:6.055938588323193e-03
Node:0,Smear_count:0,Length=6.928203,Height=2,ex_dir=3,Wilson Loop:3.240536490416562e-04
Node:0,Smear_count:0,Length=6.928203,Height=3,ex_dir=3,Wilson Loop:-3.265545649646180e-04
Node:0,Smear_count:0,Length=6.928203,Height=4,ex_dir=3,Wilson Loop:-1.129371884983702e-04

Results from second case: (swapping x and y coordinates)

Node:0,Smear_count:0,x=0,y=1,Length=1.000000,Height=1,ex_dir=3,Wilson Loop:5.415310497463935e-01
Node:0,Smear_count:0,x=0,y=1,Length=1.000000,Height=2,ex_dir=3,Wilson Loop:2.989843084939524e-01
Node:0,Smear_count:0,x=0,y=1,Length=1.000000,Height=3,ex_dir=3,Wilson Loop:1.683720211814673e-01
Node:0,Smear_count:0,x=0,y=1,Length=1.000000,Height=4,ex_dir=3,Wilson Loop:9.513755112092502e-02
Node:0,Smear_count:0,x=0,y=2,Length=2.000000,Height=1,ex_dir=3,Wilson Loop:2.988292105397755e-01
Node:0,Smear_count:0,x=0,y=2,Length=2.000000,Height=2,ex_dir=3,Wilson Loop:1.036251536262440e-01
Node:0,Smear_count:0,x=0,y=2,Length=2.000000,Height=3,ex_dir=3,Wilson Loop:3.934422556804130e-02
Node:0,Smear_count:0,x=0,y=2,Length=2.000000,Height=4,ex_dir=3,Wilson Loop:1.534567048782771e-02
Node:0,Smear_count:0,x=0,y=3,Length=3.000000,Height=1,ex_dir=3,Wilson Loop:1.683097768375253e-01
Node:0,Smear_count:0,x=0,y=3,Length=3.000000,Height=2,ex_dir=3,Wilson Loop:3.952744879497768e-02
Node:0,Smear_count:0,x=0,y=3,Length=3.000000,Height=3,ex_dir=3,Wilson Loop:1.129745493249806e-02
Node:0,Smear_count:0,x=0,y=3,Length=3.000000,Height=4,ex_dir=3,Wilson Loop:3.495959058142938e-03
Node:0,Smear_count:0,x=0,y=4,Length=4.000000,Height=1,ex_dir=3,Wilson Loop:9.509986024471435e-02
Node:0,Smear_count:0,x=0,y=4,Length=4.000000,Height=2,ex_dir=3,Wilson Loop:1.532669443767490e-02
Node:0,Smear_count:0,x=0,y=4,Length=4.000000,Height=3,ex_dir=3,Wilson Loop:3.419764739416865e-03
Node:0,Smear_count:0,x=0,y=4,Length=4.000000,Height=4,ex_dir=3,Wilson Loop:7.796308238129630e-04
Node:0,Smear_count:0,x=1,y=1,Length=1.414214,Height=1,ex_dir=3,Wilson Loop:3.478309988745993e-01
Node:0,Smear_count:0,x=1,y=1,Length=1.414214,Height=2,ex_dir=3,Wilson Loop:1.454104143113652e-01
Node:0,Smear_count:0,x=1,y=1,Length=1.414214,Height=3,ex_dir=3,Wilson Loop:6.563398152506475e-02
Node:0,Smear_count:0,x=1,y=1,Length=1.414214,Height=4,ex_dir=3,Wilson Loop:3.018583980944410e-02
Node:0,Smear_count:0,x=1,y=2,Length=2.236068,Height=1,ex_dir=3,Wilson Loop:2.207222968648315e-01
Node:0,Smear_count:0,x=1,y=2,Length=2.236068,Height=2,ex_dir=3,Wilson Loop:6.792344696820346e-02
Node:0,Smear_count:0,x=1,y=2,Length=2.236068,Height=3,ex_dir=3,Wilson Loop:2.394174427484879e-02
Node:0,Smear_count:0,x=1,y=2,Length=2.236068,Height=4,ex_dir=3,Wilson Loop:8.737576050305213e-03
Node:0,Smear_count:0,x=1,y=3,Length=3.162278,Height=1,ex_dir=3,Wilson Loop:1.269590315734095e-01
Node:0,Smear_count:0,x=1,y=3,Length=3.162278,Height=2,ex_dir=3,Wilson Loop:2.751369434715729e-02
Node:0,Smear_count:0,x=1,y=3,Length=3.162278,Height=3,ex_dir=3,Wilson Loop:7.528610445847035e-03
Node:0,Smear_count:0,x=1,y=3,Length=3.162278,Height=4,ex_dir=3,Wilson Loop:2.275467219509008e-03
Node:0,Smear_count:0,x=1,y=4,Length=4.123106,Height=1,ex_dir=3,Wilson Loop:7.302148572342397e-02
Node:0,Smear_count:0,x=1,y=4,Length=4.123106,Height=2,ex_dir=3,Wilson Loop:1.119225959266536e-02
Node:0,Smear_count:0,x=1,y=4,Length=4.123106,Height=3,ex_dir=3,Wilson Loop:2.408397375147882e-03
Node:0,Smear_count:0,x=1,y=4,Length=4.123106,Height=4,ex_dir=3,Wilson Loop:4.720684023649508e-04
Node:0,Smear_count:0,x=2,y=2,Length=2.828427,Height=1,ex_dir=3,Wilson Loop:1.421269129883017e-01
Node:0,Smear_count:0,x=2,y=2,Length=2.828427,Height=2,ex_dir=3,Wilson Loop:3.376059768522414e-02
Node:0,Smear_count:0,x=2,y=2,Length=2.828427,Height=3,ex_dir=3,Wilson Loop:1.019921049972849e-02
Node:0,Smear_count:0,x=2,y=2,Length=2.828427,Height=4,ex_dir=3,Wilson Loop:3.130921934195334e-03
Node:0,Smear_count:0,x=2,y=3,Length=3.605551,Height=1,ex_dir=3,Wilson Loop:8.468717998213722e-02
Node:0,Smear_count:0,x=2,y=3,Length=3.605551,Height=2,ex_dir=3,Wilson Loop:1.528402673868381e-02
Node:0,Smear_count:0,x=2,y=3,Length=3.605551,Height=3,ex_dir=3,Wilson Loop:3.691426209264199e-03
Node:0,Smear_count:0,x=2,y=3,Length=3.605551,Height=4,ex_dir=3,Wilson Loop:8.774445386751247e-04
Node:0,Smear_count:0,x=2,y=4,Length=4.472136,Height=1,ex_dir=3,Wilson Loop:5.393557100198080e-02
Node:0,Smear_count:0,x=2,y=4,Length=4.472136,Height=2,ex_dir=3,Wilson Loop:7.246089970549818e-03
Node:0,Smear_count:0,x=2,y=4,Length=4.472136,Height=3,ex_dir=3,Wilson Loop:1.538623074674748e-03
Node:0,Smear_count:0,x=2,y=4,Length=4.472136,Height=4,ex_dir=3,Wilson Loop:3.492485230801360e-04
Node:0,Smear_count:0,x=3,y=3,Length=4.242641,Height=1,ex_dir=3,Wilson Loop:5.883669905303618e-02
Node:0,Smear_count:0,x=3,y=3,Length=4.242641,Height=2,ex_dir=3,Wilson Loop:8.396826765200625e-03
Node:0,Smear_count:0,x=3,y=3,Length=4.242641,Height=3,ex_dir=3,Wilson Loop:1.869233003590909e-03
Node:0,Smear_count:0,x=3,y=3,Length=4.242641,Height=4,ex_dir=3,Wilson Loop:2.515534000178141e-04
Node:0,Smear_count:0,x=3,y=4,Length=5.000000,Height=1,ex_dir=3,Wilson Loop:3.519563294174048e-02
Node:0,Smear_count:0,x=3,y=4,Length=5.000000,Height=2,ex_dir=3,Wilson Loop:3.789589670139042e-03
Node:0,Smear_count:0,x=3,y=4,Length=5.000000,Height=3,ex_dir=3,Wilson Loop:7.511445102987512e-04
Node:0,Smear_count:0,x=3,y=4,Length=5.000000,Height=4,ex_dir=3,Wilson Loop:2.194875653005857e-04
Node:0,Smear_count:0,x=4,y=4,Length=5.656854,Height=1,ex_dir=3,Wilson Loop:2.442737871076606e-02
Node:0,Smear_count:0,x=4,y=4,Length=5.656854,Height=2,ex_dir=3,Wilson Loop:2.296892672336099e-03
Node:0,Smear_count:0,x=4,y=4,Length=5.656854,Height=3,ex_dir=3,Wilson Loop:3.981138036947671e-04
Node:0,Smear_count:0,x=4,y=4,Length=5.656854,Height=4,ex_dir=3,Wilson Loop:-8.436587852575061e-05
2d bresenham results end here
Node:0,Smear_count:0,Length=1.000000,Height=1,ex_dir=3,Wilson Loop:5.415310497463935e-01
Node:0,Smear_count:0,Length=1.000000,Height=2,ex_dir=3,Wilson Loop:2.989843084939524e-01
Node:0,Smear_count:0,Length=1.000000,Height=3,ex_dir=3,Wilson Loop:1.683720211814673e-01
Node:0,Smear_count:0,Length=1.000000,Height=4,ex_dir=3,Wilson Loop:9.513755112092502e-02
Node:0,Smear_count:0,Length=2.000000,Height=1,ex_dir=3,Wilson Loop:2.988292105397755e-01
Node:0,Smear_count:0,Length=2.000000,Height=2,ex_dir=3,Wilson Loop:1.036251536262440e-01
Node:0,Smear_count:0,Length=2.000000,Height=3,ex_dir=3,Wilson Loop:3.934422556804130e-02
Node:0,Smear_count:0,Length=2.000000,Height=4,ex_dir=3,Wilson Loop:1.534567048782771e-02
Node:0,Smear_count:0,Length=3.000000,Height=1,ex_dir=3,Wilson Loop:1.683097768375253e-01
Node:0,Smear_count:0,Length=3.000000,Height=2,ex_dir=3,Wilson Loop:3.952744879497768e-02
Node:0,Smear_count:0,Length=3.000000,Height=3,ex_dir=3,Wilson Loop:1.129745493249806e-02
Node:0,Smear_count:0,Length=3.000000,Height=4,ex_dir=3,Wilson Loop:3.495959058142938e-03
Node:0,Smear_count:0,Length=4.000000,Height=1,ex_dir=3,Wilson Loop:9.509986024471435e-02
Node:0,Smear_count:0,Length=4.000000,Height=2,ex_dir=3,Wilson Loop:1.532669443767490e-02
Node:0,Smear_count:0,Length=4.000000,Height=3,ex_dir=3,Wilson Loop:3.419764739416865e-03
Node:0,Smear_count:0,Length=4.000000,Height=4,ex_dir=3,Wilson Loop:7.796308238129630e-04
Node:0,Smear_count:0,Length=1.414214,Height=1,ex_dir=3,Wilson Loop:3.478524630355460e-01
Node:0,Smear_count:0,Length=1.414214,Height=2,ex_dir=3,Wilson Loop:1.452627579620166e-01
Node:0,Smear_count:0,Length=1.414214,Height=3,ex_dir=3,Wilson Loop:6.560547922366472e-02
Node:0,Smear_count:0,Length=1.414214,Height=4,ex_dir=3,Wilson Loop:3.006449758343626e-02
Node:0,Smear_count:0,Length=2.236068,Height=1,ex_dir=3,Wilson Loop:2.207222968648315e-01
Node:0,Smear_count:0,Length=2.236068,Height=2,ex_dir=3,Wilson Loop:6.792344696820346e-02
Node:0,Smear_count:0,Length=2.236068,Height=3,ex_dir=3,Wilson Loop:2.394174427484879e-02
Node:0,Smear_count:0,Length=2.236068,Height=4,ex_dir=3,Wilson Loop:8.737576050305213e-03
Node:0,Smear_count:0,Length=3.162278,Height=1,ex_dir=3,Wilson Loop:1.269590315734095e-01
Node:0,Smear_count:0,Length=3.162278,Height=2,ex_dir=3,Wilson Loop:2.751369434715729e-02
Node:0,Smear_count:0,Length=3.162278,Height=3,ex_dir=3,Wilson Loop:7.528610445847035e-03
Node:0,Smear_count:0,Length=3.162278,Height=4,ex_dir=3,Wilson Loop:2.275467219509008e-03
Node:0,Smear_count:0,Length=4.123106,Height=1,ex_dir=3,Wilson Loop:7.302148572342397e-02
Node:0,Smear_count:0,Length=4.123106,Height=2,ex_dir=3,Wilson Loop:1.119225959266536e-02
Node:0,Smear_count:0,Length=4.123106,Height=3,ex_dir=3,Wilson Loop:2.408397375147882e-03
Node:0,Smear_count:0,Length=4.123106,Height=4,ex_dir=3,Wilson Loop:4.720684023649508e-04
Node:0,Smear_count:0,Length=2.828427,Height=1,ex_dir=3,Wilson Loop:1.419193153520172e-01
Node:0,Smear_count:0,Length=2.828427,Height=2,ex_dir=3,Wilson Loop:3.370156398488239e-02
Node:0,Smear_count:0,Length=2.828427,Height=3,ex_dir=3,Wilson Loop:1.020813369097898e-02
Node:0,Smear_count:0,Length=2.828427,Height=4,ex_dir=3,Wilson Loop:3.110595408555808e-03
Node:0,Smear_count:0,Length=3.605551,Height=1,ex_dir=3,Wilson Loop:8.468717998213722e-02
Node:0,Smear_count:0,Length=3.605551,Height=2,ex_dir=3,Wilson Loop:1.528402673868381e-02
Node:0,Smear_count:0,Length=3.605551,Height=3,ex_dir=3,Wilson Loop:3.691426209264199e-03
Node:0,Smear_count:0,Length=3.605551,Height=4,ex_dir=3,Wilson Loop:8.774445386751247e-04
Node:0,Smear_count:0,Length=4.472136,Height=1,ex_dir=3,Wilson Loop:5.393557100198080e-02
Node:0,Smear_count:0,Length=4.472136,Height=2,ex_dir=3,Wilson Loop:7.246089970549817e-03
Node:0,Smear_count:0,Length=4.472136,Height=3,ex_dir=3,Wilson Loop:1.538623074674748e-03
Node:0,Smear_count:0,Length=4.472136,Height=4,ex_dir=3,Wilson Loop:3.492485230801360e-04
Node:0,Smear_count:0,Length=4.242641,Height=1,ex_dir=3,Wilson Loop:5.886688277777838e-02
Node:0,Smear_count:0,Length=4.242641,Height=2,ex_dir=3,Wilson Loop:8.357088014724416e-03
Node:0,Smear_count:0,Length=4.242641,Height=3,ex_dir=3,Wilson Loop:1.823944477897913e-03
Node:0,Smear_count:0,Length=4.242641,Height=4,ex_dir=3,Wilson Loop:2.885129031228969e-04
Node:0,Smear_count:0,Length=5.000000,Height=1,ex_dir=3,Wilson Loop:3.519563294174048e-02
Node:0,Smear_count:0,Length=5.000000,Height=2,ex_dir=3,Wilson Loop:3.789589670139042e-03
Node:0,Smear_count:0,Length=5.000000,Height=3,ex_dir=3,Wilson Loop:7.511445102987512e-04
Node:0,Smear_count:0,Length=5.000000,Height=4,ex_dir=3,Wilson Loop:2.194875653005858e-04
Node:0,Smear_count:0,Length=5.656854,Height=1,ex_dir=3,Wilson Loop:2.460185528998115e-02
Node:0,Smear_count:0,Length=5.656854,Height=2,ex_dir=3,Wilson Loop:2.280548448069865e-03
Node:0,Smear_count:0,Length=5.656854,Height=3,ex_dir=3,Wilson Loop:2.454432334364802e-04
Node:0,Smear_count:0,Length=5.656854,Height=4,ex_dir=3,Wilson Loop:-1.417845523514047e-04
Node:0,Smear_count:0,Length=1.732051,Height=1,ex_dir=3,Wilson Loop:2.323584539802566e-01
Node:0,Smear_count:0,Length=1.732051,Height=2,ex_dir=3,Wilson Loop:8.006702113996193e-02
Node:0,Smear_count:0,Length=1.732051,Height=3,ex_dir=3,Wilson Loop:3.181405632272664e-02
Node:0,Smear_count:0,Length=1.732051,Height=4,ex_dir=3,Wilson Loop:1.326117286861066e-02
Node:0,Smear_count:0,Length=2.449490,Height=1,ex_dir=3,Wilson Loop:1.538339706597785e-01
Node:0,Smear_count:0,Length=2.449490,Height=2,ex_dir=3,Wilson Loop:4.184440696907019e-02
Node:0,Smear_count:0,Length=2.449490,Height=3,ex_dir=3,Wilson Loop:1.391336201023652e-02
Node:0,Smear_count:0,Length=2.449490,Height=4,ex_dir=3,Wilson Loop:4.910984299235446e-03
Node:0,Smear_count:0,Length=3.316625,Height=1,ex_dir=3,Wilson Loop:8.942348744270423e-02
Node:0,Smear_count:0,Length=3.316625,Height=2,ex_dir=3,Wilson Loop:1.759755462346386e-02
Node:0,Smear_count:0,Length=3.316625,Height=3,ex_dir=3,Wilson Loop:4.846163955699981e-03
Node:0,Smear_count:0,Length=3.316625,Height=4,ex_dir=3,Wilson Loop:1.327808488575193e-03
Node:0,Smear_count:0,Length=4.242641,Height=1,ex_dir=3,Wilson Loop:5.191201830929035e-02
Node:0,Smear_count:0,Length=4.242641,Height=2,ex_dir=3,Wilson Loop:7.402214117360789e-03
Node:0,Smear_count:0,Length=4.242641,Height=3,ex_dir=3,Wilson Loop:1.717061134984803e-03
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