A method of S2VectorFieldHarmonic.

S2VectorFieldHarmonic.quadrature(f, bandwidth=L), from a callable or from nodes and values with their weights, MATLAB’s name for the constructor

Syntax

vF = S2VectorFieldHarmonic.quadrature(lambda v: v.cross(zvector), bandwidth=8)

Of a function returning vectors.

vF = S2VectorFieldHarmonic.quadrature(v, w, bandwidth=8, weights=wq)

Of vectors w at directions v.

Description

A function is approximated by quadrature on a grid of the bandwidth, componentwise in x, y and z; vectors at scattered directions by the quadrature sum with the weights given, which is exact only for the weights of a quadrature rule; S2VectorFieldHarmonic.interpolate fits them by least squares.

Input

f a function of vector3d returning vectors, S2VectorField, or vector3d of directions
args the vectors at the directions, and the frame of the field

Keywords

keyword default description
bandwidth None the largest harmonic degree; by default the preference ‘defaultS2Bandwidth’, for a field the field’s
weights None the quadrature weights of vectors at scattered directions, equal ones of sum 4 pi by default

Output

vF S2VectorFieldHarmonic

See also

S2VectorFieldHarmonic, S2VectorFieldHarmonic.interpolate

MATLAB’s S2VectorFieldHarmonic.quadrature

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/S2VectorFieldHarmonic.quadrature_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.