SO3FunHarmonic.evalEquispacedFFT edit page

Evaluate an SO3FunHarmonic on an equispaced grid in Euler angles \[(\alpha_a,\beta_b,\gamma_c) = (\frac{2\pi a}{H_1},\frac{\pi b}{H_2-1},\frac{2\pi c}{H_3})\] where \(a=0,...,H_1-1\), \(b=0,...,H_2-1\) and \(c=0,...,H_3-1\).

Therefore we transform the Harmonic series to an usual Fourier series equivalent as in the function eval. But we use an equispaced FFT instead of the NFFT.

Syntax

f = evalEquispacedFFT(SO3F,rot)

Input

SO3F SO3FunHarmonic
rot quadratureSO3Grid - 'ClenshawCurtis'

Output

f values at this grid points
nodes orientation

Example

construct quadrature grid and evaluate there. Output will be a unique part of this grid

SO3F = SO3FunHarmonic.example;
rot = quadratureSO3Grid(62,SO3F.CS)
v = evalEquispacedFFT(SO3F,rot);
rot = quadratureSO3Grid (Quartz → y↓→x)
  scheme: ClenshawCurtis
  bandwidth: 62
  grid: 333396 orientations
  full grid size: 42 × 125 × 126

for big grid sizes the construction of the quadrature grid is memory expansive. Hence construct struct, but the output is full sized

rot = struct('scheme','ClenshawCurtis','bandwidth',350,'CS',SO3F.CS,'SS',specimenSymmetry)
v = evalEquispacedFFT(SO3F,rot);
rot = 
  struct with fields:

       scheme: 'ClenshawCurtis'
    bandwidth: 350
           CS: [1×1 crystalSymmetry]
           SS: [1×1 specimenSymmetry]

See also

SO3FunHarmonic.eval SO3FunHarmonic.evalNFSOFT SO3FunHarmonic.SO3FunHarmonic

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/SO3FunHarmonic.evalEquispacedFFT.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.