the spherical coefficients up to bandwidth L from weighted values at directions, the direct sum below 50 nodes; a quadrature grid brings the weights of its rule

Syntax

fhat = sphericalSeriesAdjoint(v, values, 8)

The weights 1/n.

fhat = sphericalSeriesAdjoint(v, values, 8, weights=w, real=True)

Weighted, real values.

fhat = sphericalSeriesAdjoint(quadratureS2Grid(16), values, 8)

The quadrature of a grid.

Description

The internal coefficients fhat_l^m = sum_q w_q v_q conj(Y_l^m(v_q)), the adjoint of sphericalSeries; on a quadrature grid with its weights the exact coefficients of a function of that bandwidth. Every route gives the same coefficients; real chooses only the array of the NUFFT, half of it for real values, the full one otherwise.

Input

v vector3d, or a quadratureS2Grid
values the values at the directions
L the bandwidth

Keywords

keyword default description
weights None the weight of every direction; by default 1/n, or the grid’s rule
real None the NUFFT works on half its array, complex values taken as two real ones; by default when the values are real

Output

fhat the (L+1)^2 spherical coefficients, internal convention

See also

sphericalSeries, sphericalPlan

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/sphericalSeriesAdjoint_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.