the plan for a node set: the NUFFT at arbitrary nodes, the FFT on a Clenshaw-Curtis grid, the NUFFT on the nodes of a grid whose polar rule is not equispaced

Syntax

p = wignerPlan(rotation.rand(1000), 8)

The NUFFT at arbitrary rotations.

p = wignerPlan(quadratureSO3Grid(16), 8)

The FFT on a Clenshaw-Curtis grid.

p = wignerPlan(rotation.rand(1000), 8, real=False)

For complex valued functions.

f = p(F._fhat)

The series at the nodes.

fhat = p.adjoint(f, np.full(1000, 1e-3))

The adjoint with weights.

Description

A plan holds what the transform at a fixed node set needs, so that the series of many coefficient vectors or their adjoints at the same nodes cost the transform only. The coefficients are the internal ones, F._fhat.

Input

nodes rotations, or a quadratureSO3Grid
L the bandwidth

Keywords

keyword default description
real True the plan for real valued functions, which needs half the Fourier array
folds (1, 1) (rA, rB), the folds about z on the crystal and the specimen side the coefficients are known to have, which shrink the Fourier array; not read for a quadratureSO3Grid, whose own folds decide the plan

Output

plan SO3GridPlan or SO3FourierPlan, called with coefficients, plan.adjoint with values and weights

See also

wignerSeries, wignerSeriesAdjoint, sphericalPlan

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/wignerPlan_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.