A method of S2Kernel.
the derivative of a kernel on the sphere with respect to the polar angle, or to its cosine
Syntax
d = psi.grad(t)
Dpsi/dtheta at the cosines t.
d = psi.grad(v, zvector)
At the angles between the directions v and the z axis.
d = psi.grad(t, polynomial=True)
Dpsi/dt, the derivative in the cosine.
dpsi = psi.grad()
The derivative as a kernel.
Description
The kernel is a Legendre series psi(t) in the cosine t of the angle; its derivative in t is a Legendre series of its own, and the derivative in the angle theta is -sin(theta) dpsi/dt. Without an argument the result is a kernel: a handle of the angular derivative, or the Legendre series of dpsi/dt for polynomial=True.
Input
psi |
S2Kernel |
t |
ndarray of cosines, or vector3d |
other |
vector3d, the direction the angles of t are measured from |
Keywords
| keyword | default | description |
|---|---|---|
polynomial |
False |
the derivative with respect to the cosine t instead of the angle |
Output
d |
ndarray, or S2Kernel / S2KernelHandle without an argument |
See also
S2Kernel, S2FunHarmonic.grad, S2Kernels
MATLAB’s S2Kernel.grad
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/S2Kernel.grad_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.