A method of vector3d.

the inner product of two vectors, pointwise; of crystal directions the largest over their symmetric equivalents

Syntax

d = dot(v1, v2)

Pointwise, broadcast against each other.

d = dot(v1, v2, antipodal=True)

Up to sign: the absolute value.

d = dot(m1, m2, symmetry=False)

Crystal directions as they are given.

d = dot(m1, m2, min=True)

The smallest over the symmetric equivalents.

d = dot(m1, m2, all=True)

Every symmetric equivalent.

d = dot(v1, v2, outer=True)

Every pair, MATLAB’s dot_outer.

Description

An axis on either side reads the product up to sign; antipodal=True does so always, antipodal=False never. Crystal directions in a frame with symmetry give the largest product over their symmetric equivalents.

Input

v1, v2 vector3d
m1, m2 vector3d in one crystal frame

Keywords

keyword default description
antipodal None read the vectors as axes: True always, False never; by default where one of them is an axis
symmetry True take the symmetric equivalents of crystal directions into account
min False the smallest product over the symmetric equivalents instead of the largest
all False the products with every symmetric equivalent, along a new first axis
outer False every entry of v1 with every entry of v2

Output

d array, of the broadcast shape; with outer=True of shape v1.shape + v2.shape

See also

vector3d.angle, vector3d.cross, vector3d.norm

MATLAB’s vector3d.dot

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/vector3d.dot_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.