Calculates the mean value of a SO3FunHarmonic by using the first Wigner coefficient, i.e.
\[ mean(f) = \hat{f}_0^{0,0} = \frac1{8\pi^2} \int_{SO(3)} f( R ) dR \],
where \(vol(SO(3)) = \int_{SO(3)} 1 dR = 8\pi^2\).
or calculates the mean along a specified dimension of a vector-valued SO3Fun.
Description
If SO3F is a 3x3 SO3Fun then mean(SO3F) returns a 3x3 matrix with the mean values of each function mean(SO3F, 1) returns a 1x3 SO3Fun which contains the pointwise mean values along the first dimension
Syntax
value = mean(SO3F)
SO3F = mean(SO3F, d)Input
| SO3F | SO3FunHarmonic |
| d | dimension to take the mean value over |
Output
| SO3F | SO3FunHarmonic |
| value | double |
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/SO3FunHarmonic.mean.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.