a function on SO(3) as a series of Wigner functions, symmetric under its crystal and specimen frame

Syntax

SO3F = SO3FunHarmonic(fhat, cs, ss)

From MTEX’s coefficients.

SO3F = SO3FunHarmonic(odf, bandwidth=32)

The harmonic form of another function.

SO3F = SO3FunHarmonic(lambda ori: ori.angle(), cs)

A callable by quadrature.

SO3F = SO3FunHarmonic(lambda ori: ori.angle(), cs, 'GaussLegendre', bandwidth=16)

On the Gauss-Legendre grid.

SO3F = SO3FunHarmonic(psi, cs, bandwidth=24)

The series of an SO(3) kernel.

mdf = SO3FunHarmonic(lambda o: o.angle(), cs, cs, antipodal=True, bandwidth=8)

A misorientation function, f(g) = f(g^-1).

Description

What the first argument is decides how the coefficients come about:

coefficients: MTEX’s, degree by degree, deg2dim(L + 1) of them for the bandwidth L; a vector ending inside a degree block is padded with zeros to its end. An array of more axes is a list of functions, its shape in front of the coefficients.
another SO(3) function: its harmonic form at the bandwidth given; an SO3FunRBF reaches at most its kernel’s bandwidth.
an SO(3) kernel: its series.
a callable of orientations: sampled on a quadrature grid of the bandwidth, by default the preference defaultSO3Bandwidth, Clenshaw-Curtis unless ‘GaussLegendre’ is named among the frames.

The frames are the crystal frame and the specimen frame, the second by default specimenFrame.default. The coefficients are made invariant under both unless symmetrise=False.

Input

`fhat`	array of MTEX’s coefficients, an SO3Fun, an SO3Kernel or a callable of orientations
`cs, ss`	crystalFrame and specimenFrame (or a second crystalFrame)

Keywords

keyword	default	description
`real`	`None`	whether the function takes real values only; by default read off the coefficients or the sampled values
`antipodal`	`None`	f(g) = f(g^-1), the exchange symmetry of a misorientation function; needs the same frame on both sides
`symmetrise`	`True`	make the coefficients invariant under the two frames’ symmetries
`bandwidth`	`None`	the largest degree of the series
`dtype`	`None`	the complex type of the coefficients, complex128 unless given

Output

SO3F SO3FunHarmonic

Properties

`fhat`	Wigner coefficients in MTEX’s public basis
`bandwidth`	largest harmonic degree; assignment truncates or pads the expansion
`CS, SS`	crystal and specimen reference frames
`isReal`	whether the function takes real values; setting True projects onto the real part
`antipodal`	whether grain exchange symmetry f(g)=f(inv(g)) is imposed
`shape`	shape of a function list, excluding the coefficient axis

Used on

AngleDistributionFunction, ODFInversePoleFigure, RandomSampling, SO3FunHarmonicRepresentation, SingleSlipModel, PoleFigure2ODFAmbiguity, PoleFigure2ODFGhostCorrection, SO3FunConvolution, SO3FunDefinition, SO3FunOperations, SO3FunQuadrature, SO3FunSymmetricFunctions

MATLAB’s SO3FunHarmonic.SO3FunHarmonic

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/SO3FunHarmonic.SO3FunHarmonic_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.

SO3FunHarmonic.SO3FunHarmonic