A method of S2FunHarmonic.

the entropy -int f log f of a function on SO(3) or on the sphere; MATLAB’s entropy

Syntax

e = odf.entropy()

At twice the bandwidth, at least 64 (128 on the sphere).

e = odf.entropy(bandwidth=128)

The quadrature of another bandwidth.

Description

The integral is computed by the exact quadrature rule of a raised bandwidth, since f log f is not bandlimited; points where f is not positive contribute zero. On the sphere it is the mean over the sphere, as MATLAB divides by 4 pi.

Input

f SO3Fun or S2Fun

Keywords

keyword default description
bandwidth None the bandwidth of the quadrature grid, at most twice the preference maxSO3Bandwidth (maxS2Bandwidth on the sphere)

Output

e the entropy, a number

See also

textureIndex, SO3FunHarmonic.norm

MATLAB’s S2FunHarmonic.entropy

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/S2FunHarmonic.entropy_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.