the cosine of the half angle beyond which the kernel stays below tol of its peak, in closed form for the families with one and found by a scan otherwise; a kernel that never drops that far is summed in full

Syntax

c = supportCosine(psi)

Where psi falls below 1e-9 of psi(1).

c = supportCosine(psi, tol=1e-4)

A wider cut, a smaller support.

Description

The de la Vallee Poussin and von Mises-Fisher kernels have it in closed form; any other kernel is scanned on a grid of 0.5 degree in the rotation angle for the first angle from which every value stays below tol times the peak. The kernel sums of SO3FunRBF evaluate only the centres whose cosine to the query exceeds it.

Input

psi SO3Kernel

Keywords

keyword default description
tol 1e-09 the bound relative to the value at the identity

Output

c the cosine cos(omega/2) of the support’s radius, -1 when the kernel never drops below

See also

SO3FunRBF, SO3Kernel.halfwidth

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/supportCosine_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.