A method of S2Fun.

a function on the sphere through the values at the nodes, a regularised least squares fit; MATLAB’s S2FunHarmonic.interpolate

Syntax

sF = S2Fun.interpolate(v, y)

A function through values at directions.

sF = S2Fun.interpolate(v, y, bandwidth=16, lambda_=1e-4)

Of a given degree, regularised.

sVF = S2Fun.interpolate(v, w)

A vector field through vectors w.

Description

The harmonic coefficients up to the bandwidth minimise the weighted squared misfit at the nodes plus lambda_ times the Sobolev norm, solved by LSQR; the keywords, bandwidth, lambda_, s, weights, maxIter, tol and withParameters, are those of interpolate, where they are explained.

Input

nodes vector3d, the directions

Keywords

keyword default description
values None ndarray of one value per node, or vector3d for a vector field

Output

sF S2FunHarmonic, or S2VectorFieldHarmonic for vector values

See also

interpolate, S2FunHarmonic.adjoint, calcDensity

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/S2Fun.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.