the real Wigner-d matrix d_l(beta) at one angle, or with bandwidth=L the list d_0 .. d_L; MATLAB’s Wigner_d_recursion

Syntax

d = wignerd(beta, l)

The (2l+1) x (2l+1) matrix of degree l.

ds = wignerd(beta, bandwidth=L)

The matrices of the degrees 0 to L.

Description

The matrices are those of MTEX’s Wigner blocks, indexed from -l to l, computed by a stable recursion over the degrees. Give either the degree or the bandwidth.

Input

beta one angle, the second Euler angle
degree the degree l

Keywords

keyword default description
bandwidth None the largest degree L of the list

Output

d ndarray of shape (2l+1, 2l+1)
ds list of the matrices of the degrees 0 to L

See also

WignerD, SO3FunHarmonic

source

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_py.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.