A method of SO3GridPlan.

the SO(3) coefficients from weighted values on the grid, the FFTs taken backwards; without weights those of the grid’s rule

Syntax

g = quadratureSO3Grid(16)
p = SO3GridPlan(g, 8)

fhat = p.adjoint(values)

The quadrature of the grid’s rule.

fhat = p.adjoint(values, weights=g.weights)

Weights of the grid’s shape given.

Description

The values are those at the nodes of a Clenshaw-Curtis grid in its order; real values give the coefficients of a real function. With the grid’s rule the adjoint is the exact quadrature, p.adjoint(p(fhat)) = fhat for a bandwidth the grid holds. The coefficients are the internal ones, F._fhat.

Input

values the values at the grid’s nodes

Keywords

keyword default description
weights None the quadrature weights at the nodes; by default the grid’s rule in beta, the same for every alpha and gamma

Output

fhat the Wigner coefficients up to the plan’s bandwidth

See also

wignerSeriesAdjoint, wignerPlan, quadratureSO3Grid

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/SO3GridPlan.adjoint_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.