S2FunHarmonic.adjointNFSFT(v, values, bandwidth=32): the adjoint transform, the coefficients sum_j w_j y_j conj(Y(v_j)) with unit weights unless given, a grid’s own on a grid; MATLAB’s adjoint and adjointNFSFT

Syntax

sF = S2FunHarmonic.adjoint(v, values, bandwidth=16)

Unit weights.

sF = S2FunHarmonic.adjoint(v, values, bandwidth=16, weights=w)

With quadrature weights.

sF = S2FunHarmonic.adjoint(quadratureS2Grid(16), values)

A quadrature grid: its bandwidth and weights.

Description

With the weights of a quadrature rule exact up to twice the bandwidth the adjoint is the expansion of the function the values sample; with other weights it is the adjoint of the evaluation only, S2FunHarmonic.interpolate fits by least squares. A NaN value counts as 0. Several values per node, an array (n, …), give one function per column. MATLAB’s flags ‘nfsft’ and ‘directComputation’ choose the algorithm and have no counterpart; its default bandwidth is 512.

Input

`nodes`	vector3d or quadratureS2Grid
`values`	ndarray, one value or one row of values per node

Keywords

keyword	default	description
`bandwidth`	`None`	the largest harmonic degree; by default the bandwidth of the grid, else 128
`weights`	`None`	the weights of the nodes, one number or one per node; by default those of a quadrature grid, else one

Output

`sF`	S2FunHarmonic

Used on

S2FunSampling

MATLAB’s S2FunHarmonic.adjointNFSFT

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/S2FunHarmonic.adjointNFSFT_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.

S2FunHarmonic.adjointNFSFT