the maximum of a function on SO(3) or the sphere, the value and the position, numLocal local maxima from a grid refined down to the accuracy; with a second function or a number the pointwise maximum; with axis= the maximum of a list of functions along an axis; MATLAB’s max

Syntax

value, ori = max(odf)

The global maximum and where it is.

values, oris = max(odf, numLocal=5, resolution=5*degree, accuracy=0.25*degree)

The five largest local maxima.

f = max(odf1, odf2)

The pointwise maximum of two functions.

v, pos = max(sF)

On the sphere, the direction.

values, positions = max(sF, numLocal=3)

Three local maxima on the sphere.

sF = max(sF, 0.5)

The pointwise maximum with a number.

Description

The local maxima are searched from a grid of the spacing resolution (5 degree on SO(3), 2.5 on the sphere) and refined down to accuracy (0.25 and 0.05 degree); the keywords resolution, accuracy and, on SO(3), startingNodes, the orientations to start from, go to that search. Maxima closer than the resolution are merged, so fewer than numLocal can come back. A function on the circle and a pole figure take their own max. Where MATLAB writes max(SO3F, [], dim), the port writes max(SO3F, axis=dim - 1).

Input

f SO3Fun, S2Fun or S1Fun; a second function or a number for the pointwise maximum

Keywords

keyword default description
numLocal 1 the number of local maxima returned

Output

value the largest value, or numLocal values in descending order
ori the position: orientation, vector3d, or the angle on the circle

See also

min, calcComponents, SO3FunHarmonic.mean

MATLAB’s SO3Fun.max

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/SO3Fun.max_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.