a vector field on the sphere by the spherical harmonic expansions of its three Cartesian components

Syntax

vF = S2VectorFieldHarmonic(lambda v: v.cross(vector3d.Z), bandwidth=16)

A callable of the directions.

vF = S2VectorFieldHarmonic(v, w, weights=wq)

Vectors at directions, by quadrature.

vF = S2VectorFieldHarmonic([sFx, sFy, sFz])

The component functions.

vF = S2VectorFieldHarmonic(fhat, cs)

The coefficients, (L+1)^2 x 3.

vF = S2VectorFieldHarmonic(sF.grad())

The expansion of another field.

vF = S2VectorFieldHarmonic.quadrature(lambda v: v.cross(vector3d.Z))

MATLAB’s form.

Description

A callable is evaluated on a quadrature grid of the bandwidth and expanded; vectors w at directions v are expanded with the quadrature weights given, equal ones by default, which suits directions spread evenly; two component functions leave z zero. The field is projected onto the fields equivariant under the group of the frame, which a crystal frame asks for, unless symmetrise=False. vF.x, vF.y, vF.z are the components, vF.bandwidth the largest degree.

Input

`fun`	callable taking a vector3d and returning vector3d, or an S2VectorField
`v`	vector3d, the directions of given vectors
`w`	vector3d, the vectors at them
`sFx, sFy, sFz`	S2FunHarmonic, the components
`fhat`	complex array of (L+1)^2 x 3 coefficients
`cs`	crystalFrame or specimenFrame of the directions

Keywords

keyword	default	description
`bandwidth`	`None`	the largest degree of the expansion, by default the preference ‘defaultS2Bandwidth’; truncates a field given
`weights`	`None`	the quadrature weights of the directions v
`symmetrise`	`True`	project onto the fields equivariant under the group of the frame

Output

`vF`	S2VectorFieldHarmonic

Used on

S2FunVectorField

MATLAB’s S2VectorField.S2VectorField

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/S2VectorField.S2VectorField_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.

S2VectorField.S2VectorField