the contraction of tensors, vectors, rotations or arrays over the indices they share
Syntax
EinsteinSum(C, [1, 2, -1, -2], eps, [-1, -2])
Sigma_ij = C_ijkl eps_kl.
EinsteinSum(a, [1], b, [2])
The dyad a_i b_j.
EinsteinSum(T, [-1, -2, -1, -2])
A label twice in one operand is a trace.
Description
Every operand carries one label per index: a positive one is free and orders the result, a negative one is summed over. Lists of tensors combine elementwise over their leading dimensions. The result keeps the frame of the first tensor and is a plain tensor, or a number when no index is free.
Signature
EinsteinSum(*args)
Used on
AnisotropicTheory, TensorArithmetics
MATLAB’s tensor.EinsteinSum
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/tensor.EinsteinSum_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.