WignerD edit page

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))

See also

sphericalY symmetry.WignerD

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/WignerD.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX 
@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.