coefficients from weighted values: the adjoint sum below DIRECT_SUM_NODES nodes; a quadrature grid brings the weights of its rule

Syntax

fhat = wignerSeriesAdjoint(rots, values, 8)

The weights 1/n.

fhat = wignerSeriesAdjoint(rots, values, 8, weights=w)

Weighted.

fhat = wignerSeriesAdjoint(quadratureSO3Grid(16), values, 8)

The quadrature of a grid.

Description

The internal Wigner coefficients fhat_n^{kl} = sqrt(2n+1) sum_q w_q v_q conj(D_n^{kl}(R_q)) up to bandwidth L, the adjoint of wignerSeries; on a quadrature grid with its weights the exact coefficients of a function of that bandwidth. Real values give the coefficients of a real function.

Input

rots rotations, or a quadratureSO3Grid
values the values at the rotations
L the bandwidth

Keywords

keyword default description
weights None the weight of every rotation; by default 1/n, or the grid’s rule
folds (1, 1) (rA, rB), the folds about z the result is known to have, which shrink the NUFFT’s array; not read for a quadratureSO3Grid, whose own folds decide the route

Output

fhat the Wigner coefficients, internal convention

See also

wignerSeries, wignerSeriesAdjointGridded, wignerPlan

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/wignerSeriesAdjoint_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.