the Fourier array G[m, j] of spherical coefficients of bandwidth L, so that f(theta, rho) is the sum of G e^{i(m rho - j theta)}; for a real function only m >= 0, the column m = 0 halved

Syntax

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

G = sphericalTransform(f._fhat, 8)

The (2L+1) x (2L+1) array.

G = sphericalTransform(f._fhat, 8, real=True)

The rows m >= 0 of a real function.

G = sphericalTransform(f._fhat, 8, degrees=halfPiDegrees(8))

The Wigner-d matrices given.

Description

The coefficients are the port’s internal ones, f._fhat, with the Condon-Shortley phase, not MATLAB’s f.fhat. The transform is the first step of the evaluation on a grid or by the NUFFT.

Input

fhat the spherical coefficients, (L+1)^2 of them or more, those above L ignored
L the bandwidth

Keywords

keyword default description
real False the coefficients are those of a real function: only the rows m >= 0 are formed, and f is twice the real part of their sum
degrees None the pairs (n, d_n(pi/2)) as halfPiDegrees yields them; by default those of the cache, which also selects the compiled loop

Output

G the complex array, (L+1) x (2L+1) for a real function, (2L+1) x (2L+1) otherwise

See also

sphericalTransformAdjoint, sphericalSeries, halfPiDegrees

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/sphericalTransform_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.