A method of SO3Kernel.

the Chebyshev coefficients A_0 .. A_L of the kernel, to its bandwidth by default; MATLAB’s calcFourier

Syntax

A = psi.calcFourier()

Up to the bandwidth of the kernel, psi.A.

A = psi.calcFourier(64)

Up to the degree 64.

Description

The kernel is the series psi(cos(omega/2)) = sum_n A_n U_2n(cos(omega/2)) of Chebyshev polynomials of the second kind; the coefficients come in closed form or by a recurrence for the kernel families and by quadrature for a kernel given as a function. MATLAB’s ‘GaussKronrod’ and maxAngle are not taken.

Input

psi SO3Kernel

Keywords

keyword default description
L None the largest degree, the bandwidth of the kernel when not given

Output

A ndarray of L + 1 coefficients

See also

SO3Kernel.eval, S2Kernel.calcFourier, S1Kernel.calcFourier

MATLAB’s SO3Kernel.calcFourier

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/SO3Kernel.calcFourier_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.