A method of S1FunHarmonic.

the Fourier series of a function on the circle by quadrature; MATLAB’s approximate and quadrature

Syntax

sF = S1FunHarmonic.quadrature(lambda x: np.sin(2*x))

A callable on the grid of the bandwidth.

sF = S1FunHarmonic.quadrature(lambda x: np.sin(2*x), bandwidth=16)

To another bandwidth.

sF = S1FunHarmonic.quadrature(x, values, bandwidth=16, weights=w)

Values at given angles.

Description

A callable is sampled on the equispaced quadrature grid of the bandwidth, which makes the coefficients exact up to that degree; values at given angles are summed with the weights, the coefficient c_k = sum_j w_j f(x_j) e^{ikx_j}, which is the quadrature only when the weights are those of a quadrature rule for the angles (1/n for n equispaced ones). The bandwidth is by default the preference maxS1Bandwidth. S1FunHarmonic.approximate is the same function.

Input

x a callable of the angle, or an array of angles in radians

Keywords

keyword default description
values None the values at the angles x
bandwidth None the largest degree of the series
weights None the quadrature weights of the angles
real None whether the function takes real values only; by default whether the values are real

Output

sF S1FunHarmonic

See also

S1FunHarmonic, S1FunHarmonic.interpolate, SO3FunHarmonic.quadrature

MATLAB’s S1FunHarmonic.approximate

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/S1FunHarmonic.approximate_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.