A method of S2AxisFieldHarmonic.

the least squares fit to axes at directions: the six components of v v^T one by one; MATLAB’s S2AxisFieldHarmonic.interpolate

Syntax

aF = S2AxisFieldHarmonic.interpolate(v, a)

An axis field through axes a at directions v.

aF = S2AxisFieldHarmonic.interpolate(v, a, bandwidth=8, lambda_=1e-3)

Of a given degree, regularised.

Description

Each of the six components of the matrices a a^T is fitted by interpolate, a regularised least squares fit, and the field evaluates to the leading eigenvector of the fitted matrix. Further keywords, lambda_, s, maxIter and tol, go to interpolate.

Input

nodes vector3d, the directions
values vector3d, the axes at the directions

Keywords

keyword default description
bandwidth None the largest harmonic degree; by default it follows from the number of nodes
weights None the weights of the nodes, as interpolate takes them

Output

aF S2AxisFieldHarmonic

See also

interpolate, S2AxisFieldHarmonic.quadrature, S2VectorFieldHarmonic.interpolate

MATLAB’s S2AxisFieldHarmonic.interpolate

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/S2AxisFieldHarmonic.interpolate_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.