the Bingham distribution fitted to directions or axes, with the confidence ellipse of its modal axis

Syntax

f = S2FunBingham.fit(v)

The fitted distribution.

f = S2FunBingham.fit(v, weights=w)

Weighted directions.

f, ab, rot = S2FunBingham.fit(v, confidenceEllipse=True, p=0.95)

With the confidence ellipse.

Description

The eigen decomposition of the scatter matrix of the directions, sum of w v v^T, gives the axes of the distribution, and Newton’s method on the moments its shape parameters, ascending to zero at the third axis, the mode. A direction and its antipode count alike.

The confidence ellipse of the modal axis is the asymptotic covariance of the largest eigenvector, Tanaka’s: its semi-axes ab in radians and the rotation rot turning the z axis onto the mode, drawn by ellipse(rot, ab[0], ab[1]).

Input

`v`	vector3d or Miller, the directions or axes

Keywords

keyword	default	description
`weights`	`None`	the weights of the directions, equal by default
`confidenceEllipse`	`False`	return also ab and rot, MATLAB’s second and third output
`p`	`0.95`	the confidence level of the ellipse

Output

`f`	S2FunBingham, in the frame of v
`ab`	the two semi-axes of the confidence ellipse in radians
`rot`	rotation, the position of the confidence ellipse

References

H. Tanaka, Circular asymmetry of the paleomagnetic directions observed at low latitude volcanic sites, Earth Planets Space 51 (1999) 1279-1286

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/S2FunBingham.fit_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.

S2FunBingham.fit