compute reciprocal basis vectors from a direct crystal basis

Syntax

dual = reciprocalAxes(axes)

Description

Rows of axes are the Cartesian vectors a, b and c. Return rows a*, b* and c* such that axes @ dual.T is the identity. No factor 2*pi is included. Reciprocal lengths use the inverse of the direct-basis units. A degenerate basis has no finite reciprocal basis.

Input

axes numeric array of shape (3, 3), one direct basis vector per row

Output

dual array of shape (3, 3), one reciprocal basis vector per row

See also

crystalFrame.basisDual, Miller

Signature

reciprocalAxes(axes)
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/reciprocalAxes_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.