the series at every rotation of a container or on a quadrature grid; the direct sum below DIRECT_SERIES_NODES nodes (DIRECT_SUM_NODES without numba), and a grid that cannot hold the bandwidth is evaluated at its nodes

Syntax

F = SO3FunHarmonic(unimodalODF(orientation.rand(crystalFrame('1'))), bandwidth=8)

f = wignerSeries(F._fhat, rotation.rand(10))

The values at rotations, as F.eval.

f = wignerSeries(F._fhat, quadratureSO3Grid(16))

On a grid, by the FFT.

f = wignerSeries(F._fhat, rotation.rand(10), real=False)

The complex values.

Description

The sum of sqrt(2n+1) fhat_n^{kl} D_n^{kl}(R) over the degrees n up to the bandwidth of the internal coefficients F._fhat; the route, the direct sum, the FFT of a Clenshaw-Curtis grid or the NUFFT, is chosen by the number of nodes. The result has the shape of the rotations.

Input

fhat the internal Wigner coefficients
rots rotations, or a quadratureSO3Grid

Keywords

keyword default description
real None whether the coefficients are those of a real function, whose values are returned real; by default isRealWigner(fhat)
folds (1, 1) (rA, rB), the folds about z the coefficients have, which shrink the NUFFT’s array; not read for a quadratureSO3Grid, whose own folds decide the route

Output

f the values at the rotations, real for real coefficients

See also

wignerSeriesAdjoint, wignerPlan, SO3FunHarmonic.eval

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/wignerSeries_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.