invert a rotation, tensor or spatial transform.
Syntax
inverse = inv(x)
Description
For an MTEX object, inv(x, …) calls x.inv(…). Additional positional and keyword arguments are passed to that method unchanged. Its documentation specifies the accepted inputs, units, symmetry handling and optional outputs. Consult the corresponding method for the behaviour of a particular object type.
For numeric arrays without an MTEX method, this calls numpy.linalg.inv.
Signature
inv(x, *args, **kwargs)
Methods it calls
| complianceTensor | the inverse: rank two by the matrix, rank four through the Voigt matrix, which swaps the convention and with it the class, a stiffness inverting to a compliance |
| orientation | reverse the direction of an orientation mapping |
| orthogonalTransform | the inverse transform, the inverse rotation with the same parity |
| quaternion | return the multiplicative inverse of each quaternion |
| rotation | return the rotation that reverses each input rotation |
| SO3FunHarmonic | form the function evaluated at inverse rotations |
| SO3FunRBF | the inverse function f(g^-1), the centres inverted, crystal and specimen sides exchanged |
| SO3VectorFieldHarmonic | the push-forward under R -> R^-1: a left vector v at R becomes the right vector -v at R^-1, so inv(grad f) = grad(inv f) |
| spatialTransform | the inverse transform |
| spatialTransformComposite | the inverses of the stages in reverse order |
| spatialTransformDrift | the inverse by fixed point iteration |
| spatialTransformField | the inverse by fixed point iteration |
| spatialTransformHandle | the transform of the inverse function, an error where none was given |
| spatialTransformId | the identity itself |
| spatialTransformInverse | the transform it inverts |
| spatialTransformPoly | the inverse: the inverse affine map at degree 1, the fixed point inverse at degree 2 |
| spatialTransformProjective | the homography of the inverse matrix |
| spatialTransformRigid | the translation by -u |
| spatialTransformShift | the affine map of the inverse matrix |
| spatialTransformTilt | the inverses of the stages in reverse order, a plain composite |
| stiffnessTensor | the inverse: rank two by the matrix, rank four through the Voigt matrix, which swaps the convention and with it the class, a stiffness inverting to a compliance |
| tensor | the inverse: rank two by the matrix, rank four through the Voigt matrix, which swaps the convention and with it the class, a stiffness inverting to a compliance |
Used on
DefinitionAsCoordinateTransform, MTEXvsBungeConvention, OrientationInversePoleFigure, EBSDSharpPlot, EBSDSpatialTransform, AnisotropicTheory, IsotropicTheory, NotationAndConventions, BoundaryProperties, BoundarySelect, MisorientationGrainExchangeSym, MisorientationTheory
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/inv_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.