the SO(3) coefficients up to bandwidth L from weighted values, every rotation rounded to the nearest node of a Clenshaw-Curtis grid and the grid’s FFT adjoint taken, MATLAB’s ‘gridded’; approximate, and its cost independent of the number of rotations

Syntax

fhat = wignerSeriesAdjointGridded(rots, values, 8)

The weights 1/n.

fhat = wignerSeriesAdjointGridded(rots, values, 8, weights=w, folds=(2, 1))

Weighted, a twofold axis.

Description

The weighted values are summed at the nearest node of a Clenshaw-Curtis grid of bandwidth min(2L, max(L, 128)) and the grid’s exact adjoint taken; the error is at most half the grid’s spacing, which a kernel of bandwidth L hardly sees. MATLAB’s SO3FunHarmonic.adjoint(…, ‘gridded’).

Input

rots rotations
values the values at the rotations
L the bandwidth

Keywords

keyword default description
weights None the weight of every rotation; by default 1/n
folds (1, 1) (rA, rB), the folds about z of the result, which the grid then covers only the folded region of

Output

fhat the Wigner coefficients, internal convention

See also

wignerSeriesAdjoint, SO3FunHarmonic.adjoint

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/wignerSeriesAdjointGridded_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.