the mean angular deviation of a list of rotations from their mean

Syntax

sigma = std(rot)

The deviation in radians.

sigma = std(rot, robust=True)

From the robust mean.

sigma = std(rot, weights=w)

From the weighted mean.

Description

The root mean square of the rotational angles between the mean and every rotation; for orientations the angle is the symmetry reduced one, as the mean is. The weights enter the mean only, not the average of the angles.

Input

rot quaternion, rotation or orientation

Keywords

keyword	default	description
`weights`	`None`	one weight per rotation, for the mean
`robust`	`False`	deviation from the robust mean, outliers left out of the mean
`axis`	`None`	NumPy’s reduction axis, refused: the deviation is over the whole list
`dtype`	`None`	NumPy’s argument, refused
`out`	`None`	NumPy’s argument, refused
`keepdims`	`False`	keep the reduced axes with length one, as np.std does
`ddof`	`0`	NumPy’s degrees of freedom, refused

Output

sigma the deviation in radians

Used on

TiltAndTwistBoundaries, HarmonicApproximationTheory, RBFApproximationTheory, SO3FunApproximationTheory, SO3FunConvolution

MATLAB’s quaternion.std

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/quaternion.std_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.

quaternion.std