the antiderivative of a gradient field, the function of mean zero whose gradient it is

Syntax

f = antiderivative(SO3VF)

The function, an SO3FunHarmonic.

values = antiderivative(SO3VF, x)

Its values at orientations x.

f = antiderivative(SO3VF, conservative=True)

Without checking the field is a gradient.

Description

The function is the inverse Laplacian of the divergence of the field, defined up to a constant, which is chosen to give mean zero. A field that is no gradient is refused unless conservative says it is one: the gradient of the result must give the field back within tol relative to its norm.

Input

SO3VF SO3VectorField, converted to its harmonic form
x orientation, where to evaluate the antiderivative

Keywords

keyword default description
conservative False the field is known to be a gradient, so it is not checked
tol 0.0001 the relative tolerance of the check

Output

f SO3FunHarmonic
values array, the values at x

See also

grad, div, curl, SO3VectorFieldHarmonic, SO3FunVectorField

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/antiderivative_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.