A method of tensor.
the mean of a list of tensors, over all of them or along axes, weighted or not; with an ODF or orientations the texture average
Syntax
T = T.mean()
The mean over the whole list.
T = T.mean(axis=1)
Along the second axis, MATLAB’s mean(T, 2).
T = T.mean(weights=w)
The weighted mean.
TReuss = T.mean('Reuss')
The inverse of the mean of the inverses.
THill = T.mean('Hill')
The mean of the Voigt and Reuss means.
TVoigt, TReuss, THill = T.mean('all')
The three averages at once.
TVoigt = T.mean(odf)
The texture average over an ODF.
TVoigt, TReuss, THill = T.mean(odf, 'all')
Its three averages.
TVoigt = T.mean(ori, weights=w)
The average over weighted orientations.
Description
The plain mean is MATLAB’s Voigt average; MATLAB’s three outputs are asked for by name, ‘all’. With an ODF or orientations the mean is calcTensor’s, the single crystal tensor rotated by the orientations and averaged. NumPy’s np.mean(T) and np.mean(T, axis=1) call it. The density of tensors of different densities is averaged with them. MATLAB’s ‘geometric’ mean is not there.
Input
T |
tensor |
odf |
SO3Fun, the texture average over it |
ori |
orientation, the texture average over them |
Keywords
| keyword | default | description |
|---|---|---|
weights |
None |
one weight per tensor, or per orientation |
axis |
None |
the axis or tuple of axes of the list to average along |
dtype |
None |
NumPy’s argument, refused unless None |
out |
None |
NumPy’s argument, refused unless None |
keepdims |
False |
keep the averaged axes with length one |
Output
T |
tensor, the mean; TVoigt, TReuss, THill the three averages |
See also
calcTensor, tensor.sum, TensorAverage
MATLAB’s tensor.mean
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.mean_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.