a vector field on SO(3) whose three components are series of Wigner functions, in the left or the right tangent space

Syntax

SO3VF = SO3VectorFieldHarmonic(fhat, cs, ss, 'left')

From a coefficient matrix.

SO3VF = SO3VectorFieldHarmonic(F, 'right')

Another field in the right tangent space.

SO3VF = SO3VectorFieldHarmonic(F, bandwidth=8)

Another field cut to a bandwidth.

SO3VF = SO3VectorFieldHarmonic(t, bandwidth=8)

Through tangent vectors t at orientations.

SO3VF = SO3VectorFieldHarmonic([F1, F2, F3])

From its three component functions.

SO3VF = SO3VectorFieldHarmonic(lambda ori: F(ori), cs, ss, bandwidth=8)

A callable by quadrature.

Description

A field in the left tangent space returns its tangent vectors in the specimen frame, one in the right tangent space in the crystal frame; ‘left’ unless named. Another field given is converted to the side named.

The field is built from:

a coefficient matrix: the components as columns of MTEX’s coefficients, made equivariant under the frames unless symmetrise=False.
tangent vectors t at reference orientations: summed with the weights against the Wigner functions, a quadrature only for the weights of a quadrature rule.
a callable of orientations: sampled on a quadrature grid of the bandwidth, by default the preference defaultSO3Bandwidth.
three component functions: their coefficients, cut to the largest bandwidth, and their frames unless cs and ss are given.

Input

`fhat`	(deg2dim(L + 1), 3) array, an SO3VectorField, an SO3TangentVector, three SO3FunHarmonic or a callable of orientations
`cs, ss`	crystalFrame and specimenFrame

Keywords

keyword	default	description
`bandwidth`	`None`	the largest degree of the components
`weights`	`None`	the weights of the tangent vectors, equal unless given
`symmetrise`	`True`	make a coefficient matrix equivariant under the frames’ symmetries

Output

SO3VF SO3VectorFieldHarmonic

Used on

SO3FunVectorField

MATLAB’s SO3VectorFieldHarmonic.SO3VectorFieldHarmonic

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/SO3VectorFieldHarmonic.SO3VectorFieldHarmonic_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.

SO3VectorFieldHarmonic.SO3VectorFieldHarmonic