calculate an inner product, with the symmetry conventions of its operands.
Syntax
value = dot(v, w)
Description
For an MTEX object, dot(x, …) calls x.dot(…). 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.dot.
Signature
dot(x, *args, **kwargs)
Methods it calls
| embedding | the inner product of two embeddings of the same crystal frame, image by image |
| orientation | the dot product up to symmetry, cos(omega/2) of the misorientation angle omega reduced over the groups of both frames |
| orthogonalTransform | the inner product of the rotational parts up to sign, zero between transforms of different parity |
| quaternion | the inner product of the coefficients |
| rotation | the inner product up to sign, since q and -q are one rotation |
| S1FunHarmonic | the inner product with g for the normalised measure, by the coefficients |
| S2AxisFieldHarmonic | the cosine of the angle to a constant axis, sqrt(x^T (a a^T) x), and to another field |
| S2FunHarmonic | the inner product with another function of the same frame, for the normalised surface measure: int conj(f) g dS / 4 pi |
| S2VectorFieldHarmonic | the inner product with a constant vector, exact, a function without the group |
| SO3FunHarmonic | the inner product int conj(f) g, the first argument conjugated |
| SO3Grid | the dot product up to symmetry, cos(omega/2) of the misorientation angle omega reduced over the groups of both frames |
| SO3TangentVector | the inner product with tangent vectors at the same reference, brought to this side |
| SO3VectorFieldHarmonic | the inner product with a constant vector, exact, a function on the component frames |
| SO3VectorFieldRBF | the pointwise inner product: with another field a function on SO(3), with a constant vector a function on the component frames |
| vector3d | the inner product of two vectors, pointwise |
Used on
CrystalOperations, LatticeMetric, WaveVelocities, SO3FunVectorField, S2FunHarmonicRepresentation, S2FunVectorField, MagneticAnisotropy, VectorsOperations
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/dot_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.