the Chebyshev coefficients of a kernel, or the harmonic power of a function, per degree; MATLAB’s plotSpektra

Syntax

plotSpectrum(psi)

The Chebyshev coefficients of a kernel.

plotSpectrum(psi, bandwidth=16, logarithmic=True)

The absolute values, on log-log axes.

plotSpectrum(odf)

The harmonic power of an SO3Fun.

plotSpectrum([odf1, odf2], bandwidth=20)

One line per function.

odf.plotSpectrum()

The same, as a method.

Description

What is drawn depends on the input:

a kernel on S2 or SO(3): the coefficients A_l / (2l + 1) over the degree l, on a logarithmic degree axis, up to degree 32 unless the bandwidth says otherwise. With logarithmic=True their absolute values on log-log axes.
a function on S2 or SO(3): the power of every degree, the norm of its coefficients, as open circles on a dotted line, up to the bandwidth of the function. A function of another kind is first expanded into harmonics; logarithmic changes nothing.
a function on the circle: the norm of the coefficients of k and -k over |k|, drawn the same way.
a list: one line per entry, in one axes.

The other keywords are those of a line plot; fontSize sets the size of the labels and ticks.

Input

`x`	an S2Kernel or SO3Kernel, an S1Fun, S2Fun or SO3Fun, or a list of them

Keywords

keyword	default	description
`bandwidth`	`None`	the highest degree drawn
`logarithmic`	`False`	a kernel’s absolute coefficients on log-log axes

Output

`h`	the matplotlib lines drawn, a list of them for a list

Used on

ODFShapes, SO3FunHarmonicRepresentation, Annotations, PoleFigure2ODFAmbiguity, PoleFigure2ODFGhostCorrection, PoleFigureSantaFe, HarmonicApproximationTheory, SO3FunConvolution, SO3FunDefinition, SO3FunVectorValued, SO3Kernels, S2FunHarmonicRepresentation

MATLAB’s SO3Fun.plotSpektra

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.plotSpektra_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.

SO3Fun.plotSpektra