construct an n-point Clenshaw–Curtis quadrature rule on [-1, 1]

Syntax

x, w = clenshawCurtis(n)
integral = np.sum(w * fun(x))

Description

Nodes are cos(pi*b/(n-1)) for b from zero to n-1, including both endpoints. Weights integrate polynomials through degree n-1 exactly, apart from rounding, and sum to 2. For n=1 the single node is zero with weight 2.

Input

n positive integer node count

Output

x nodes in descending order
w quadrature weights corresponding to x

See also

gaussLegendre, quadratureS2Grid

Signature

clenshawCurtis(n)
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/clenshawCurtis_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.