A method of SO3FunHarmonic.

the distance between two orientation density functions, or the error of an ODF against pole figures

Syntax

e = calcError(odf1, odf2)

Half the mean absolute difference.

e = calcError(odf1, odf2, 'l2', resolution=2.5*degree)

The relative L2 error on a finer grid.

e = calcError(odf, pf, 'RP')

The RP error against pole figures.

Description

Two functions are compared at the nodes of an equispaced grid of the resolution in the fundamental region of f; their crystal groups and their specimen groups must be of the same Laue class. The mode chooses the measure:

  • ‘l1’, the default: half the mean absolute difference. For two densities it is the fraction of the volume that would have to move to turn one into the other, between 0 and 1.
  • ‘l2’: the norm of the difference over the norm of g, on the grid; MATLAB computes it from the harmonic series.

With pole figures second the result is PoleFigure.calcError, one number per pole figure, with its own modes (‘relative’, the default, ‘RP’, ‘l1’, ‘l2’) and the threshold epsilon. MATLAB’s ‘L0’, the volume where the two differ by more than epsilon, is not provided.

Input

f SO3Fun
g SO3Fun, or PoleFigure
mode ‘l1’ or ‘l2’ for two functions, ‘relative’, ‘RP’, ‘l1’ or ‘l2’ with pole figures

Keywords

keyword default description
resolution 5*degree the spacing of the grid on which two functions are compared
epsilon None the threshold of the error against pole figures

Output

e float, or one float per pole figure

See also

PoleFigure.calcError, calcODF, PoleFigure2ODF

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/SO3FunHarmonic.calcError_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.