equally spaced angles and weights for Fourier quadrature on the circle

Syntax

grid = quadratureS1Grid(16)
x = grid.nodes()
average = np.sum(grid.weights * fun(x))

Description

For bandwidth L the grid has 2*L+2 nodes in [0, 2*pi), excluding the repeated endpoint. Equal weights sum to one and integrate Fourier modes through degree 2*L+1 exactly. Multiply the weighted mean by 2*pi for the usual angular integral.

Input

`bandwidth`	nonnegative integer harmonic bandwidth L
`dtype`	floating-point type for nodes and weights; default np.float64

Output

grid quadratureS1Grid

Properties

`bandwidth`	requested harmonic bandwidth
`x`	node angles in radians
`weights`	equal normalised weights

Members

nodes	the nodes, 2L+2 equispaced angles in [0, 2 pi)
weights	the quadrature weights, all equal and summing to one

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/quadratureS1Grid_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.

The class quadratureS1Grid