the adjoint: fhat_l^m = sqrt((2l+1)/4pi) i^m sum_j d_l^{jm} d_l^{j0} h[m, -j] for h[m, j] = sum_q w_q v_q e^{-i(m rho_q - j theta_q)}

Syntax

fhat = sphericalTransformAdjoint(H, 8)

H of shape (2L+1) x (2L+1).

fhat = sphericalTransformAdjoint(H, 8, real=True)

H of the rows m >= 0 of a real function.

Description

The adjoint of sphericalTransform: the internal spherical coefficients (with the Condon-Shortley phase, not MATLAB’s fhat) from the Fourier array of weighted values. For a real function only the rows m >= 0 are read and the coefficients of negative order follow by symmetry.

Input

H the complex array h[m, j]
L the bandwidth

Keywords

keyword default description
real False H holds the rows m >= 0 of a real function
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

fhat the (L+1)^2 spherical coefficients

See also

sphericalTransform, sphericalSeriesAdjoint, 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/sphericalTransformAdjoint_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.