reusable transform plan for a Wigner series at arbitrary rotations

Syntax

plan = SO3FourierPlan(ori, L)
values = plan(fhat)
coefficients = plan.adjoint(values, weights)

Description

Evaluation maps internal Wigner coefficients to values at the nodes. The adjoint maps weighted node values to coefficients; for scattered nodes it is an adjoint sum, rather than a least-squares inverse. Reusing a plan avoids rebuilding transform data for each coefficient vector. setNodes updates the query rotations.

The folds option specifies invariance under rotations about z on the crystal and specimen sides. Coefficients outside those symmetry index sets must vanish; transforms then use the reduced index sets. Public SO3FunHarmonic.fhat coefficients must be converted to the internal convention before using this low-level plan directly.

Input

rots rotation or orientation nodes
L maximum Wigner degree; coefficient arrays have length deg2dim(L+1)
real use the transform for real-valued functions; default True
folds crystal and specimen z-rotation orders; default (1, 1)
eps requested numerical accuracy; None uses the transform tolerance for the dtype
upsampfac NUFFT oversampling factor; None uses the configured preference

Output

plan SO3FourierPlan

See also

SO3FunHarmonic, SO3GridPlan, wignerSeries

Members

adjoint coefficients from weighted values at the nodes
setNodes moves the plan to other rotations, the finufft plans kept
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/SO3FourierPlan_index_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.