a pointwise operation on vector fields on SO(3), as a field or a function

Syntax

u = mapField(np.cross, v, w)

The cross product of two fields.

f = mapField(np.multiply, v, w, reduce=True, invariant=True)

The inner product, a function on the full frames.

u = mapField(np.multiply, v, F, bandwidth=8)

A field times a scalar function.

u = mapField(np.multiply, v, 2)

A field times a number.

Description

The arguments are evaluated on a quadrature grid, op is applied to the arrays of values and the result is expanded again. op sees a field as an (n, 3) array of tangent vectors in the tangent space of v, a function as an (n, 1) column, which broadcasts against them, and a number as itself.

An (n, 3) result is a field in the tangent space of v, one value per node a function. A function lives on the component frames of v, the frames with the symmetry on the tangent side stripped, unless invariant=True puts it on the full frames of the field.

The bandwidth of the result is the sum of those of the operands, at most the preference maxSO3Bandwidth.

Input

op a callable of NumPy arrays
v SO3VectorField
args further SO3VectorField, SO3Fun or numbers, on the frames of v

Keywords

keyword default description
bandwidth None the bandwidth of the result
invariant False put a scalar result on the frames of the field rather than its component frames
reduce False sum the result over the three components before it is expanded

Output

u SO3VectorFieldHarmonic
f SO3FunHarmonic

See also

SO3VectorFieldHarmonic, grad, antiderivative, SO3FunVectorField

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/mapField_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.