Interpolate an S2FunHarmonic by given function values at given points on the sphere.
Let \(M\) spherical points \(v_i\) and corresponding function values \(y_i\) be given. We compute the S2FunHarmonic \(f\) of an specific bandwidth which minimizes the least squares problem
\[\sum_{i=1}^M|f(v_i)-y_i|^2.\]
Syntax
sF = S2FunHarmonic.interpolate(nodes, val)
sF = S2FunHarmonic.interpolate(nodes, val, 'bandwidth', bandwidth, 'tol', TOL, 'maxit', MAXIT, 'weights', W)
sF = S2FunHarmonic.interpolate(nodes,val,'regularization',0) % no regularization
sF = S2FunHarmonic.interpolate(nodes,val,'regularization',1e-4,'SobolevIndex',2)
[sF,lsqrParameters] = S2FunHarmonic.interpolate(___)Input
| nodes | vector3d (grid on sphere) |
| val | function values on the grid (may be multidimensional) |
Options
| bandwidth | maximum degree of the spherical harmonics used to approximate the function |
| tol | tolerance for lsqr |
| maxit | maximum number of iterations for lsqr |
| weights | weight w_n for the node nodes (default: Voronoi weights) |
See also
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/S2FunHarmonic.interpolate.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.