A method of S2FunHarmonic.

the projection onto the functions invariant under the group of the frame, or under a list of rotations forming a group the frame does not name; an axis valued function is even; MATLAB’s symmetrise

Syntax

sF = symmetrise(sF)

Under the group of the frame of sF.

sF = symmetrise(sF, crystalFrame('432'))

Under the group of another frame, the result in that frame.

sF = sF.symmetrise(rotation.byAxisAngle(zvector, np.arange(4)*90*degree))

The mean over a group of rotations.

Description

Each degree is averaged over the group, the mean of the Wigner matrices of its rotations applied to the coefficients, which keeps exactly the invariant part. A frame given puts the function in that frame, which names the group. MATLAB’s symmetrise(sF, d) about a direction, returning a kernel, has no counterpart.

Input

sF S2FunHarmonic

Keywords

keyword default description
rots None rotation of a group, or a crystalFrame or specimenFrame whose group is taken

Output

sF S2FunHarmonic

See also

S2FunHarmonic.eval, Miller.symmetrise

MATLAB’s S2FunHarmonic.symmetrise

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/S2FunHarmonic.symmetrise_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.