Evaluation of Wigner-D functions or Wigner-d functions of specific degrees.
Syntax
Dl = WignerD(g,l)
Dl = WignerD(g,l,'normalize')
Dl = WignerD(g,'degree',l)
D = WignerD(g,'bandwidth',l)
dl = WignerD(beta,l)
dl = WignerD(beta,'degree',l)
d = WignerD(beta,'bandwidth',l)
C = WignerD(g,'kernel',psi)Input
| g | quaternion / rotation / orientation / symmetry |
| beta | second Euler angle in [0,pi] |
| psi | SO3Kernel |
Output
| Dl | Wigner-D matrix D_l^(m,n) (\((2l+1) \times (2l+1)\)) |
| D | all evaluated Wigner-D functions up to bandwidth L (\((l(2*l--1)(2*l+1)/3) \times n\) where n is the number of rotations) |
| dl | Wigner-d matrix d_l^(m,n) |
| d | all evaluated Wigner-d functions up to bandwidth L |
Options
| bandwidth | harmonic degree of series expansion |
| degree | number or array, single degree reshapes result |
| kernel | SO3Kernel, weights every degree by its Chebyshev coefficient and, unless a bandwidth is given, sets the bandwidth to the kernel's own. With it, |
| WignerD(ori,'kernel',psi) | |
| is the harmonic expansion of the radial basis function psi centered in ori, i.e. calcFourier(SO3FunRBF(ori,psi,1)) up to the L2 normalization conj(.)/sqrt(2n+1) per degree. | |
Flags
| normalize | l2 normalized Wigner-D functions (multiply by \sqrt(2n+1)) |