the spherical harmonic series fhat at directions or on a quadrature grid, the trigonometric sum or the NUFFT by the number of nodes

Syntax

f = S2FunHarmonic(lambda v: v.z**2, bandwidth=8)

y = sphericalSeries(f._fhat, vector3d.rand(100))

The values, as f.eval.

y = sphericalSeries(f._fhat, quadratureS2Grid(16))

On a grid, by the FFT.

y = sphericalSeries(f._fhat, vector3d.rand(100), real=False)

The complex values.

Description

The coefficients are the internal ones, f._fhat, with the Condon-Shortley phase, not MATLAB’s f.fhat. The result has the shape of the directions.

Input

fhat the spherical coefficients
v vector3d, or a quadratureS2Grid

Keywords

keyword default description
real None whether the coefficients are those of a real function, whose values are returned real; by default isRealSpherical(fhat)

Output

y the values at the directions, real for real coefficients

See also

sphericalSeriesAdjoint, sphericalPlan, S2FunHarmonic.eval

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/sphericalSeries_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.