a coefficient vector is real valued when fhat_n^{-k,-l} = (-1)^{k-l} conj(fhat_n^{kl}) on SO(3), fhat_l^{-m} = (-1)^m conj(fhat_l^m) on S2, c_{-k} = conj(c_k) on S1

Syntax

isRealWigner(F._fhat)

Whether the SO(3) coefficients are those of a real function.

isRealWigner(F._fhat, tol=1e-6)

With a looser tolerance.

Description

Whether internal Wigner coefficients, F._fhat of an SO3FunHarmonic, belong to a real valued function, every pair compared up to the relative tolerance.

Input

fhat the Wigner coefficients

Keywords

keyword default description
tol 1e-10 the tolerance, relative to the size of a coefficient where it exceeds one

Output

isReal bool

See also

isRealSpherical, isRealFourier, wignerSeries

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/isRealWigner_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.