A method of rotation.

the discrepancy between two densities and/or weighted point sets on the sphere (S2Fun, vector3d) or on SO(3) (SO3Fun, rotation, orientation), in either order; MATLAB’s discrepancy

Syntax

d = discrepancy(v, w, weights=c, weights2=e)

D_2, the root cap or ball L2 discrepancy.

d = discrepancy(sF, v, metric='D_cap', numCenters=4097)

The finite search for the largest cap.

d = discrepancy(odf, ori, metric='D_ball', numRadii=513)

The largest ball on SO(3).

d = discrepancy(sF, v, metric='L2', bandwidth=32)

A bandlimited L2 norm, ‘E_L’ the same.

d = discrepancy(sF, v, squared=True)

The square.

d, info = discrepancy(sF, v, info=True)

With what was computed.

d = discrepancy(sF, v, metric='kernel', bandwidth=16)

The squared objective of optimalSample.

Description

The measures on the sphere go to sphericalDiscrepancy, those on SO(3) to rotationalDiscrepancy, with the keywords given (weights, weights2, bandwidth, degreeWeights, the search sizes, squared, info); their pages describe the metrics. metric=’kernel’ is MATLAB’s discrepancy: the squared kernel distance of the restricted distance kernel over the degrees 1 to bandwidth, which optimalSample minimises; it takes only weights, weights2 and bandwidth, and info.

Input

a, b S2Fun or vector3d on the sphere, SO3Fun or rotation on SO(3)

Keywords

keyword default description
metric 'D_2' ‘D_2’, ‘D_cap’ or ‘L2’ (‘E_L’) on the sphere, ‘D_2’, ‘D_ball’ or ‘L2’ on SO(3), or ‘kernel’, MATLAB’s measure

Output

d the discrepancy
info with info=True, what was computed

See also

sphericalDiscrepancy, rotationalDiscrepancy, optimalSample, discreteSample

MATLAB’s rotation.discrepancy

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/rotation.discrepancy_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.