A method of S1FunHarmonic.

global, local and pointwise maxima of a function on the circle

Syntax

v, pos = max(sF)

The global maximum and the angle it is taken at.

v, pos = max(sF, resolution=1*degree)

Searched on a coarser sampling.

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

The three largest local maxima.

sF = max(sF, 0.5)

The pointwise maximum with a constant.

sF = max(sF1, sF2, bandwidth=64)

The pointwise maximum of two functions.

Description

The function is sampled at the resolution, the discrete local maxima are refined by a ternary search, and the largest numLocal are returned with the values descending: a pair of numbers for numLocal 1, else two arrays. With a number or a second function the result is the pointwise maximum as a Fourier series, by quadrature at the larger bandwidth of the two unless bandwidth is given. MATLAB’s vector valued form max(sF, [], dim) and its options kmax, startingNodes, tolerance and maxStepSize are not taken.

Input

sF, sF1, sF2 S1FunHarmonic

Keywords

keyword default description
numLocal 1 the number of local maxima to return
resolution 0.004363323129985824 the spacing of the sampling the maxima are searched on
bandwidth None the bandwidth of the pointwise maximum

Output

v, values the largest values
pos, positions the angles, in radians, they are taken at
sF S1FunHarmonic, the pointwise maximum

See also

S1FunHarmonic.min, SO3FunHarmonic.max

MATLAB’s S1Fun.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/S1Fun.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.