measure vector lengths, tensor magnitudes or function L2 norms.
Syntax
magnitude = norm(x)
Description
For an MTEX object, norm(x, …) calls x.norm(…). 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.norm.
Signature
norm(x, *args, **kwargs)
Methods it calls
| embedding | the Euclidean norm of every image |
| quaternion | the norm of the quaternions, sqrt(a^2 + b^2 + c^2 + d^2) |
| S1FunHarmonic | the L2 norm for the normalised measure, the Euclidean norm of the coefficients |
| S1Kernel | the L2 norm of the kernel, the Euclidean norm of its two sided coefficients |
| S2FunHarmonic | the L2 norm for the normalised surface measure, or the Sobolev norm, one per function |
| S2Kernel | the L2 norm of the kernel, sqrt(sum_n A_n^2 / (2n+1)) |
| S2VectorFieldHarmonic | the length at every direction, a function on the sphere, as MATLAB’s norm |
| SO3FunCBF | the L2 norm of the function, from its harmonic expansion |
| SO3FunHarmonic | the L2 norm, or the Sobolev norm sqrt(sum (2n+1)^{2s} |fhat_n|^2) |
| SO3FunRBF | the L2 norm of the function, from its harmonic expansion |
| SO3Kernel | the L2 norm of the kernel, the Euclidean norm of its coefficients |
| SO3VectorFieldHarmonic | the length of the vectors as a function on SO(3), the same as abs |
| SO3VectorFieldRBF | the length of the vectors as a function on SO(3), the same as abs |
| spatialTransform | the length of the displacement at every position |
| strainTensor | the Frobenius norm of every tensor, over all its coefficients |
| tensor | the Frobenius norm of every tensor, over all its coefficients |
| vector3d | the length of the vectors |
Used on
LatticeMetric, OrientationEmbeddings, SpecimenSymmetry, Grains3DProperties, EBSDGrid, EBSDSpatialTransform, WaveVelocities, Properties, GrainSmoothingAdvanced, EllipseBasedParameters, ProjectionBasedParameters, MisorientationDistributionFunction
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/norm_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.