A method of S1FunHarmonic.

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

Syntax

v, pos = min(sF)

The global minimum and the angle it is taken at.

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

The three smallest local minima.

sF = min(sF, 0)

The pointwise minimum with a constant.

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

The pointwise minimum of two functions.

Description

The function is sampled at the resolution, the discrete local minima are refined by a ternary search, and the smallest numLocal are returned with the values ascending: a pair of numbers for numLocal 1, else two arrays. With a number or a second function the result is the pointwise minimum as a Fourier series, by quadrature at the larger bandwidth of the two unless bandwidth is given. MATLAB’s vector valued form min(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 minima to return
resolution 0.004363323129985824 the spacing of the sampling the minima are searched on
bandwidth None the bandwidth of the pointwise minimum

Output

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

See also

S1FunHarmonic.max, SO3FunHarmonic.min

MATLAB’s S1Fun.min

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.min_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.