A method of SO3FunHarmonic.

the L2 norm, or the Sobolev norm sqrt(sum (2n+1)^{2s} fhat_n ^2)

Syntax

t = norm(SO3F)

The L2 norm, the texture index.

t = norm(SO3F, s=1)

The Sobolev norm of index 1.

Description

By Parseval’s equality the L2 norm sqrt(1/(8 pi^2) int |f(R)|^2 dR) is the Euclidean norm of the Wigner coefficients, the Wigner functions being normalised; MATLAB calls it the texture index. With a Sobolev index s every degree n is weighted by (2n+1)^{2s}.

Input

SO3F SO3FunHarmonic, a single function or a list

Keywords

keyword default description
s None the Sobolev index; None or 0 for the L2 norm

Output

t float, or an array of the shape of the list

See also

SO3FunHarmonic.mean, textureIndex

MATLAB’s SO3FunHarmonic.norm

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/SO3FunHarmonic.norm_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.