symmetry projection blocks for harmonic coefficients, stored on their nonzero index support

Description

Usually obtained from invariantProjection(frame, bandwidth). For degree n, only harmonic orders divisible by the group’s z-axis fold can contribute. Reduced blocks store those orders, avoiding multiplication by the known zero rows and columns. A trivial rotational group needs no stored projection matrices.

This is a low-level representation used by the harmonic transforms. Use invariantProjection to construct it from a reference frame rather than assembling blocks by hand.

Input

fold integer order of the group’s rotation about z
blocks reduced projection matrices, one per harmonic degree
held optional existing projection sharing the stored nonzero structure

Properties

fold retained z-axis fold
blocks reduced projection blocks

See also

invariantProjection, projectLeft, projectRight

Members

bandwidth the highest degree the held projection blocks reach
isIdentity whether the projection is the identity, the group acting through the identity alone
nonzeros the entries of the blocks above rounding level as flat lists over the degrees, degree n at ptr[n]:ptr[n+1], with block indices: what the compiled projection visits
support the indices an r fold about z leaves at degree n, k = 0 mod r, as block indices
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/InvariantProjection_index_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.